Saturday, September 23, 2017
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Seminars of the Department: Room 2NO6, Campus Plaine
Tuesday, September 19, 2017 at 2:00 PM
New theoretical uncertainties in predicting (d,p) cross sections
Natasha Timofeyuk
(d,p) reactions are a popular tool of extracting spectroscopic information about nuclei. However, this information is affected by theoretical uncertainties of (d,p) cross sections predicted by widely-used codes based on certain direct reactions theories. In this talk I will describe a recent work at Surrey that aims to incorporate a realistic feature of nucleon optical potentials - nonlocality - into existing (d,p) theories accounting for deuteron breakup. This work has revealed a high sensitivity of (d,p) cross sections to deuteron wave function at very small separation between neutron and proton when nonlocal optical potentials are used thus creating new theoretical uncertainties. I will also talk about how including energy-dependence of nonlocal optical potentials adds to theoretical uncertainties and briefly mention an ongoing investigation clarifying the role of NNN forces in (d,p) reactions.
Monday, July 10, 2017 at 2:30 PM
Nuclear structure and reactions from lattice simulations: The present and future
Dean J. Lee
I describe recent progress and future directions for lattice simulations of nuclear structure and reactions. Some of the topics include the adiabatic projection method for scattering and reactions, the connection between nuclear forces and nuclear structure, and the isotopic dependence of nuclear clustering.
Thursday, February 16, 2017 at 11:00 AM
Correlated-Gaussian approach to quantum many-body problems
Wataru Horiuchi
The correlated Gaussian (CG) method is flexible to describe complex few-body dynamics, e.g., describing different types of structure and correlated motion of the particles, eliminating the forbidden components, and accurately describing the tail of the wave function in the asymptotic region. The method has been applied to not only in nuclear physics but also other quantum mechanical fields (See recent review [1]). Here we present our progress and recent applications of the CG method: (i) 16O as a 12C+n+n+p+p five-body model [2], and (ii) a fully microscopic six-body calculation for 6He [3]. (iii) Applications to kaonic nuclear and atomic systems [4,5].
References
[1] J. Mitroy et al., Rev. Mod. Phys. 85, 693-749 (2013).
[2] W. Horiuchi and Y. Suzuki, Phys. Rev. C 89, 011304(R) (2014).
[3] D. Mikami, W. Horiuchi, and Y. Suzuki, Phys. Rev. C 89, 064303 (2014).
[4] S. Ohnishi, W. Horiuchi, T. Hoshino, K. Miyahara, and T. Hyodo, arXiv: 1701.07589.
[5] T. Hoshino, S. Ohnishi, and W. Horiuchi, in preparation.
Tuesday, February 16, 2016 at 2:00 PM
Intermediate-energy direct nuclear reactions with the Eikonal model
Pang Danyang
A new nuclear physics facillity, the High Intensity heavy-ion Accelerator Facility (HIAF), will be built in the HuiZhou City of Sourth China in the near future. HIAF will provide radioactive beams with energies from around 100 MeV to GeV per nucleon, which is the region where the Eikonal model will be very useful. In this talk we discuss the applications of the Eikonal model to three types of direct nuclear reactions which might be useful tools for the new facility: 1) the elastic scattering and breakup reactions for the single-particle structure of weakly-bound nuclei with the ratio method of Prof. Pierre Capel, 2) the intermediate-energy (p,d) reactions for studying tensor force effects in atomic nuclei, and 3) heavy-ion charge-exchange reactions for Fermi and Gamov-Teller strength in nuclei.
Tuesday, December 08, 2015 at 11:00 AM
Shape invariance and equivalent mixed Jacobi-Trudi formulas for exceptional orthogonal polynomials
Yves Grandati
We establish that the X-Hermite and X-Laguerre polynomials are amenable of Jacobi-Trudi type formulas and interpret the equivalence relations between these determinantal representations as the most general manifestation of shape invariance for the rational extensions of the harmonic and isotonic potentials.
Monday, September 07, 2015 at 10:30 AM
Hyperspherical formalism and its applications to bosonic systems
Natasha Timofeyuk
A general method to solve the many-body in hyperspherical coordinates is described. The method uses the link between the matrix elements in hyperspherical harmonics basis and those calculated traditionally in shell model and configuration interaction method. Convergence of the method is discussed for bosonic systems interacting by soft two-body and three-body forces. Application of the method to study universality in binding energies of these systems in the limit of large scattering length is presented.
Monday, May 18, 2015 at 2:30 PM
Phase transition in exactly solvable BEC models from Bethe Ansatz equations
Ian Marquette
In recent years, exactly solvable and integrable Bardeen-Cooper-Schrieffer (BSC) and Bose-Einstein condensate (BEC) have attracted a lot of attention. They have applications in superconductivity, nuclear and atomic physics. Moreover, their study is also connected with various areas of pure and applied mathematics and in particular the quantum inverse scattering method and algebraic Bethe Ansatz. I will discuss how exactly solvable models provide a unique method, via qualitative changes in the distribution of the ground-state roots of the Bethe Ansatz equations, to identify quantum phase transitions. This is an approach that has been applied in recent years in context of BCS models and I will discuss how in a recent paper we expanded the method, for two models of Bose-Einstein condensates. The first model deals with the interconversion of bosonic atoms and molecules. The second is the two-site Bose-Hubbard model, widely used to describe tunneling phenomena in Bose-Einstein condensates. For these systems we calculate the ground-state root density. This facilitates the determination of analytic forms for the ground-state energy, and associated correlation functions through the Hellmann-Feynman theorem. These calculations provide a clear identification of the quantum phase transition in each model. The talk is based on: J.Links and I.Marquette, Ground-state Bethe root densities and quantum phase transitions, J.Phys. A: Math. Theor. 48 045204 (2015), arXiv: 1409.5484
Tuesday, January 06, 2015 at 11:00 AM
Describing radiative captures from the No-Core Shell Model with Continuum
Jeremy Dohet-Eraly
Radiative captures play an important role in the synthesis of elements in the stars, in particular in the sun. The rates of these reactions are essential for describing quantitatively the evolution of the stars. However, in most stars, these radiative capture processes take place at low energies, which are out of reach of the experiments. Hence, nuclear models are required to provide accurate radiative capture cross sections at these energies. In this talk, I'll present the No-Core Shell Model with Continuum (NCSMC) and its recent extension to the study of radiative captures. The NCSMC is an ab initio approach which provides accurate solutions of microscopic Schrödinger equations based on realistic internucleon interactions. This is a powerful tool for describing both bound states and scattering states. Preliminary results for the 3He(alpha,gamma)7Be and 3H(alpha,gamma)7Li radiative cross sections obtained within this approach will be presented.
Tuesday, December 16, 2014 at 2:30 PM
Systematics of Elastic and Inelastic Deuteron Breakup
B.V. Carlson
Deuteron-induced reactions are being used to produce medical radioisotopes [1] and as surrogates to other reactions (see review [2] and references therein), among recent applications. Although they have been studied for decades [3-6], the complexity of these reactions continues to make their theoretical description challenging. The direct reaction mechanism is a major contributor to the reaction cross section due to the low binding energy of the deuteron. Competition between elastic breakup, absorption of only a neutron or a proton (stripping and inelastic breakup) and absorption of the deuteron must be taken into account to determine the formation or not of a compound nucleus and its subsequent decay. The inelastic breakup reactions – those in which either only a neutron or a proton is absorbed – are particularly complex, as they form compound nuclei with a wide range of excitation energies and angular momenta. We present the results of a theoretical study of elastic and inelastic deuteron breakup for a large selection of targets at incident deuteron energies below 100 MeV. We use the zero-range post-form DWBA approximation to calculate the elastic breakup cross section [3,4] and its extension to absorption channels to calculate the inelastic breakup cross sections [5,6]. We discuss the regularities and ambiguities in our results, as well as the irregularities in the inelastic breakup energy and angular momentum distributions that complicate their substitution by a smooth distribution obtained from systematics. References [1] E.Betak et al, Technical Reports Series 473, "Nuclear Data for the Production of Therapeutic Radionuclides", IAEA, Vienna, Austria, 2011, ISBN 978-92-0-115010-3. [2] J.E. Escher, J.T. Burke, F.S. Dietrich, N.D. Scielzo, I.J. Thompson, and W.Younes, Rev. Mod. Phys. 84, 353 (2012). [3] G. Baur and D. Trautmann, Phys. Rep. 25, 293 (1976). [4] G. Baur, F. Rösel, D. Trautmann and R. Shyam, Phys. Rep. 111, 333 (1984). [5] A. Kasano and M. Ichimura, Phys. Lett. B115, 81 (1982).
Friday, December 05, 2014 at 11:00 AM
Some recent developments in the description of breakup, removal, and knockout reactions of unstable nuclei
Kazuyuki Ogata
In this contribution some recent results on breakup, removal, and knockout reactions of unstable nuclei are briefly reviewed. Topics covered are 1) decay mode of the first 2+ state of 6He populated by nuclear breakup processes, 2) one and two neutron removal cross sections of 6He, 3) a prescription for extracting the electric dipole (E1) breakup cross section from reaction observables, 4) extension of reaction models with eikonal approximation toward relatively low incident energies, and 5) asymmetry of parallel momentum distribution of the reaction residue of (p,2p) processes. References Y. Kikuchi, T. Matsumoto, K. Minomo, and K. Ogata, PRC88, 021602 (2013). K. Minomo, T. Matsumoto, K. Egashira, K. Ogata, and M. Yahiro, PRC90, 027601 (2014). K. Yoshida, T. Fukui, K. Minomo, and K. Ogata, Prog. Theor. Exp. Phys. 2014, 053D03 (2014). T. Fukui, K. Ogata, and P. Capel, PRC90, 034617 (2014). K. Ogata, K. Yoshida, and K. Minomo, in preparation.
Thursday, November 27, 2014 at 2:30 PM
Three-body radiative capture reactions and four-body CDCC calculations using an analytical THO basis: Application to 9Be
Jesús Casal Berbel
The structure of the Borromean nucleus 9Be will be discussed within a three-body approach (alpha+alpha+n) using the analytical transformed harmonic oscillator (THO) method. The three-body formalism provides an accurate description of the radiative capture reaction rate for the entire temperature range relevant in Astrophysics. We also include the three-body model in a four-body CDCC formalism in order to describe reactions induced by 9Be. This can be a powerful tool to extract information from scaterring data.
Friday, June 27, 2014 at 11:00 AM
New developments in understanding the theory of (d,p) reactions
Natasha Timofeyuk
The progress in development of radioactive beam facilities and the methods of particle detections made it possible to measure cross sections of transfer reactions A(d,p)B in inverse kinematics. Such reactions are at the frontier of the research into evolution of the single-particle structure of nuclei with changing neutron to proton ratio. The conclusions about this structure are often deduced from the comparison between the measured (d,p) cross sections and the predictions from reaction theory. At present, many experimental groups use distorted wave Born approximation (DWBA) developed in 1960s. In this approximation many parts of exact scattering wave function are neglected. For (d,p) reactions these neglected parts include the components in which the wave function of d+target is represented by the p+n+A continuum. The simplest way to deal with it is to use adiabatic approximation developed by Johnson and Soper in early 1970s. Such an approximation allows the same DWBA codes to be used. What has not been realised until very recently is that the scheme employed by the adiabatic approach has to be modified because of non-locality of the n-A and p-A interactions in the p+n+A components. In this talk I will present the breakthrough in the development of the theory of (d,p) reactions made at Surrey over the last two years that accounts for fundamental property of quantum systems, their non-locality. I will show that non-locality can change the interpretation of the data in terms of both absolute and relative spectroscopic factors. A very useful feature of new method is that it can still employ the old DWBA codes that nuclear experimentalists have got used to.
Monday, June 16, 2014 at 11:00 AM
Exotic structure in light neutron-rich nuclei
Naoyuki Itagaki
I discuss the appearance of exotic cluster structure in light nuclei. For instance, linear chain structure of three and four alpha clusters has been widely discussed. Linear chain corresponds to highly excited state, and to stabilize this state, especially to prevent the bending motion, quite strong mechanism must exist. In this seminar I discuss three candidates; 1) adding valence neutrons, 2) orthogonalizing to the low-lying states, 3) giving large angular momentum to the system. Here I show the results based on not only cluster models but also mean-field models. Next I discuss unified description for the shell and cluster aspects of light nuclei. Recently we found a simple transformation from the so-called Brink type cluster model wave function to the jj-coupling shell model one by introducing only two parameters, which describe the distance among clusters and breaking of clusters. In 12C, the energy optimal state is just in between the cluster and shell limits, and this optimal wave function has 99 % squared overlap with that of the antisymmetrized molecular dynamics.
Wednesday, March 19, 2014 at 2:30 PM
Present State and prospect for Theoretical Study of Transfer Reaction
Tokuro Fukui
First, we introduce our work which determines the astrophysical factor of 8B(p,gamma)9C by using the transfer reaction, 8B(d,n)9C. Namely the breakup effects of the projectile and the residual nucleus in the transfer reaction are discussed. Second, we propose how to probe the alpha-cluster probability in the surface region of nuclei, where the cluster develops, via an alpha-transfer reaction. It should be noted that this probability is different from the spectroscopic factor which have been determined by conventional works, and the asymptotic normalization coefficient (ANC). Finally, if time permits, the description of transfer reactions which reproduce unbound states (unbound nuclei or excited states of bound nuclei) is given.
Friday, March 14, 2014 at 2:00 PM
Running over elastic phase shifts and jumping onto ANCs
Oscar Leonardo Ramirez Suarez
The ANC or asymptotic normalization constant together with the bound-state energy are all the information that one needs to describe the asymptotic behavior of a bound state. This behavior is important to describe radiative-capture reactions which play a crucial role in stellar evolution. Contrary to the bound-state energy, the ANC cannot be measured experimentally and therefore, in order to estimate it, theoretical calculation in agreement with relevant experimental data should be performed. In this talk I will introduce a new proposal to extract ANCs directly from experimental elastic phase shifts. This proposal is supported by the properties of the scattering matrix and the effective range function, and shows clearly that no potential model is required. Instead, experimental phase shifts and bound-state energies are the only input data necessary. Finally, I will discuss some open questions and perspectives.
Thursday, November 07, 2013 at 11:00 AM
Non-Hermitian Hamiltonian with real spectra and some of its consequences
Bikashkali Midya
In this talk after a brief review of the properties of non-Hermitian Hamiltonian with real spectra, I shall discuss the existence and stability of localized modes in complex PT -symmetric optical media described by non-linear Schroedinger equation. Exact analytical expressions of the localized modes will be shown to exist in both one-dimensional and two-dimensional geometry with self-focusing and self-defocusing nonlinearity. Linear stability analysis however reveals that some of these nonlinear modes are always unstable, although the corresponding linear Schroedinger eigenvalue problem possesses unbroken PT -symmetry.
Thursday, October 24, 2013 at 11:00 AM
Testing pairing correlations via two-particle transfer reactions
Andrea Vitturi
I will discuss the connection between pairing correlations and two-particle transfer reactions. The different aspects arising in stable and unstable nuclei, light and heavy projectiles, low and higher bombarding energies, collective and non-collective states, normal and superfluid systems, will be analyzed. As examples of the spectroscopic possibilities offered by two-particle transfer processes I will consider the case of the excited 0+ states in 32Mg and 68Ni, involving possible shell evolution and islands of inversion. In the case of weakly-bound systems the role of continuum states and the connection with two-particle break-up processes will be illustrated. Special attention will be finally given to the possible excitation of high-lying pairing correlated states, namely the Giant Pairing Vibrations.
Monday, June 17, 2013 at 2:30 PM
Fusion, breakup and elastic scattering of weakly bound nuclei
Gomes P.R.S.
In the last years one has asked whether the complete fusion induced by light weakly bound projectiles, particularly halo nuclei, is enhanced or suppressed when compared with the situation where there is no-breakup process. There are two kinds of effects to be investigated. The first is static effects, caused by the longer tail of the optical potential, owing to the low binding energies of the weakly bound and specially halo nuclei. The second kind of effect is the dynamic, which is due to the strong coupling between the elastic channel and the continuum states representing the breakup channel. Recent systematic results have shown that the dynamics effects due to breakup and transfer processes enhance the fusion cross section at sub-barrier energies and suppress it at energies above the barrier for stable and neutron-halo nuclei, although for proton-halo systems the behavior is not very clear. Also, the elastic scattering of weakly bound nuclei do not show the usual energy dependence of the optical model known as Threshold Anomaly (TA), but rather a different behavior called Breakup Threshold Anomaly (BTA). In this talk I will discuss the systematic results and the main open aspects in the field.
Friday, May 31, 2013 at 2:30 PM
Electron Screening, Non-extensive Statistics, and Dark Matter
Carlos Bertulani
I discuss a model for visible matter-dark matter interaction based on the exchange of a massive gray boson: the Mulatto. A close study of big bang nucleosynthesis (BBN), baryon asymmetries, cosmic microwave (CMB) bounds, galaxy dynamics, together with the Standard Model assumptions, help us to set a limit on the mass and width of the new gauge boson. Modification of the statistics underlying the kinetic energy distribution of particles during the BBN is considered, as well as the changes in reaction rates during the BBN due to a departure from the Debye-Hueckel electron screening model.
Wednesday, May 22, 2013 at 11:00 AM
Realizations of polynomial algebras as deformed oscillator algebras and superintegrability
Ian Marquette
We will review results on quadratic algebras with three generators and their realizations as deformed oscillator algebras. We will discuss how such realizations allow to obtain finite dimensional unitary representations of such quadratic algebras. Such algebraic results have been applied to the Smorodinky-Winternitz and also the Hartmann potential related withring shaped molecule in order to obtain algebraically the energy spectrum of these quantum systems. We will present recent results and discuss how realizations as deformed oscillator algebras can be obtained for cubic algebras, quartic algebras and also higher order polynomial algebras. We will apply these results on a superintegrable system with a second and a fourth order integrals, wavefunctions related to exceptionnal orthogonal polynomials
Tuesday, January 15, 2013 at 2:00 PM
Spectroscopy of the excited nonstrange baryons in a relativistic chiral quark model
Ergash Tursunov
The spectrum of the SU(2) flavor baryons (N and Delta states) is calculated in the frame of a relativistic chiral quark potential model. The parameters of the mean field linear confinement and Coulomb like vector potentials are fixed from the QCD study in the literature. The contribution of the gluon and pseudoscalar meson fields are included at the second order level. It is shown that the chiral constraint derived from one-pion exchange mechanism between valence quarks can help to solve the "missing resonance problem" in excited baryon spectroscopy. The convergence of the self-energy was obtained for the valence quark states up to and including 1D
_{5/2}
. At low energy scale below 2000 MeV, the obtained numerical estimations for the SU(2) baryon states (up to and including F-wave N
^{*}
and Delta
^{*}
resonances) are at the level of the relativized constituent quark model and in a reasonable agreement with the experimental data.
Wednesday, October 31, 2012 at 10:30 AM
Could quantum decoherence and measurement be deterministic phenomena? Analysis of the collision between an alpha particle and an obstacle
Aylin Manço et Jean-Marc Sparenberg
The quantum decoherence phenomenon, in particular during a measurement, displays an apparently unavoidable random character. A simple interpretation of that apparent randomness is proposed, in which the outcome of a quantum measurement is actually deterministically determined by the microscopic state of the measurement apparatus, which can thus be seen as a hidden variable. This microscopic state being inaccessible in practice, the outcome of a decoherent process cannot easily be predicted, though it is deterministic in essence. This interpretation of quantum mechanics thus restores determinism and causality at a fundamental level. In the first part of the seminar (10h30-11h10), A. Manço will test these conjectures on a primitive model of measurement process inspired by Mott [1]: the detection of a spherical alpha-particle wave in a cloud chamber. In that system, the microscopic state of the measurement apparatus is determined by the molecule positions in the chamber. In the framework of A. Manço's research-initiation grant, Mott's model was revisited in the case of a single molecule. The calculation is based on a coupled-channel Born approximation. In the second part of the seminar (11h10-11h30), J.-M. Sparenberg will explore some consequences of this interpretation. First, its compatibility with Bell's inequalities is checked; it is shown to violate these inequalities and to fully agree with standard quantum mechanics. The price to pay for that is a strong non locality. Being deterministic and non local, this interpretation is then shown to violate special relativity and to possibly allow faster-than-light information transfer. The second part of the seminar was recently presented by J.-M. Sparenberg at the Time Machine Factory 2012 conference in Torino. A short, subjective and informal account of this conference will also be given to those interested at the end of the seminar. [1] Mott, N. F. (1929). "The wave mechanics of alpha-ray tracks". Proceedings of the Royal Society A126: 79-84
Tuesday, September 18, 2012 at 2:30 PM
Unified studies of molecular structures and reactions in light neutron-excess systems
Makoto Ito
Cluster structures are important in neutron-excess systems, which are extensively investigated in recent studies. In neutron-excess systems, cluster cores are surrounded by excess neutrons, and neutrons play glue-like roles among cluster cores. In my seminar, I will show the formation of the chemical-bonding-like structures in Be isotopes, which are obtained by adding valence neutrons to the unbound two alpha cores in 8Be. In the low-lying states, neutrons occupy the covalent orbits spreading over two alpha cores, but they change to the atomic or ionic orbits, corresponding to the dimer of He isotopes. These chemical bonding states are mainly realized in continuum energy region. The unified treatment of the chemical bonding structures and reactions will be presented.
Thursday, July 05, 2012 at 2:30 PM
Relativistic R Matrix and Its Application to RIA and QHD
Janina Grineviciute
The R matrix formalism of Lane and Thomas1 has been extended to the relativistic case so that the many-coupled channels problem may be solved for systems in which binary breakup channels satisfy a relative Dirac equation. The formalism was applied to the relativistic impulse approximation2 (RIA) and also to Quantum Hadrodynamics3 (QHD) in the continuum Tamm-Dancoff approximation (TDA) with the classical meson fields replaced by one-meson exchange potentials using Dirac oscillator basis functions4,5 . It was shown6, that the common local density approximation7 (LDA) for the exchange terms was inadequate in relativistic calculations. The discrepancy between the exact and the LDA calculations was traced to the extreme difference between the matrix elements of the negative energy states of the basis functions and is therefore a relativistic effect. Application of the formalism to the relativistic continuum TDA calculations for 16O showed8 that the simple σ + ω + ρ exchange with QHD coupling constants provides reasonable agreement with experimentally determined single particle energies and
^{15}
N(p,p) cross section at 39.84 MeV9 and hence is a justifiable interaction for later use in knockout reactions. To investigate a role of pions one would need a better approximation than the effective mass approximation10 for pseudovector matrix elements.
1. A. M. Lane and R. G. Thomas, Rev. Mod. Phys. 30, 257 (1958).
2. C. J. Horowitz, Phys. Rev. C 31, 1340 (1985).
3. B. D. Serot and J. D. Walecka, Advances in Nuclear Physics, ed. by J. W. Negele and E. Vogt (Plenum, NY, 1986).
4. Ito, K. Mori and E. Carriere, Nuovo Cimento A 51, 1119 (1967).
5. M. Moshinsky and A. Szczepaniak, J. Phys. A 22, L817 (1989).
6. J. Grineviciute and D. Halderson, Phys. Rev. C 80, 044607 (2009).
7. F. A. Brieva and J. R. Rook, Nucl. Phys. A 291, 317 (1977).
8. J. Grineviciute and D. Halderson, Phys. Rev. C 85, 054617 (2012).
9. J. L. Snelgrove and E. Kashy, Phys. Rev. 187, 1259 (1969).
10. R. J. Furnstahl, Ph.D. Dissertation, Stanford University, 1985; Phys Lett. B 152, 313 (1985)
Wednesday, June 06, 2012 at 10:30 AM
Microscopic description of the α + N, α +
^{3}
He and α + α collisions
Jeremy Dohet-Eraly
The α + N, α +
^{3}
He and α + α elastic scattering is studied in a cluster model approach by the generator coordinate method coupled with the microscopic R-matrix method. In this model, α and
^{3}
He are described by one Slater determinant of Gaussian functions. The adopted nucleon-nucleon interaction is derived from the realistic Argonne potential AV18 with the unitary correlation operator method. The unitary correlation is designed to reproduce the α + α elastic phase shifts within this cluster model. The elastic phase shifts for the α + N and α +
^{3}
He collisions are calculated within the same model. Without further adjustment, a good agreement with experimental data is obtained within a small model space.
Wednesday, May 02, 2012 at 10:30 AM
The molecular ion H
^{+}
_{2}
Horacio Olivares Pilon
The H
^{+}
_{2}
molecular ion is the simplest molecular system which exists in nature. Even though the system is non-solvable, an approximate solution is proposed. Combining the WKB expansion at large distances and perturbation theory at small distances a compact uniform approximation for eigenfunctions is constructed. Total energies and some expectation values are presented and compared with new and existing data for internuclear distances R within [0,50] a.u.
Wednesday, April 18, 2012 at 10:30 AM
No-Core Shell Model with the Continuum
Simone Baroni
The proximity of the continuum in loosely bound nuclei could strongly affect all their features. A common theoretical description of both nuclear structure and scattering properties is then necessary. Coupling the No-Core Shell Model with the continuum (NCSMC) leads to a promising ab-initio method for the description of low-energy nuclear reactions. It naturally extends the already successful NCSM/RGM technique, increasing its predictive power and allowing theory to make predictions for oncoming experiments. We will discuss the first NCSMC results for nucleon scattering on light nuclei.
Wednesday, February 08, 2012 at 11:00 AM
Development of CDCC
Takuma Matsumoto
The unstable nuclei have exotic properties such as the halo structure and the island of inversion. As a feature of reactions induced by unstable nuclei, the projectile easily breaks up into its constituents. In order to extract information of the exotic properties via breakup reactions, an accurate treatment of breakup processes is highly desirable. One of the most reliable methods for treating breakup processes in the wide range of incident energies is the continuum-discretized coupled-channels method (CDCC). CDCC has successfully been applied to analyses of three-body breakup systems, in which the projectile breaks up into two constituents. Recently, we developed CDCC to describe four-body breakup systems with a three-body projectile, and proposed a new calculation for breakup cross sections of many-body projectiles by using the complex-scaling method. In this seminar, I show the validity of the new calculation of breakup cross sections in analyses of
^{6}
He breakup reactions. Furthermore, I also introduce recent development of CDCC and its applications.
Wednesday, January 11, 2012 at 10:30 AM
Core excitations in halo nuclei within a particle-rotor model using a transformed oscillator basis
José Lay
An accurate description of reactions involving weakly-bound nuclei, such as halo nuclei, requires the inclusion of the coupling to the continuum (i.e., unbound) states of the weakly-bound system. For two-body projectiles, a successful technique to describe these processes is the Continuum-Discretized Coupled-Channels (CDCC) method. In this method, the continuum is replaced by a discrete set of functions, each of them representative of a region of the continuum relevant for the reaction. The standard CDCC method uses an average of the scattering two-body wavefunctions in each energy interval (named "bin"). Alternatively, the continuum spectrum can be described by the eigenstates of the Hamiltonian in a basis of square-integrable functions, or pseudo-states (PS). In this contribution we present a PS basis obtained performing a simple analytic local scale transformation to the harmonic oscillator basis (THO). This THO basis is easy to calculate and reproduces a wide variety of observables, requiring a small number of functions compared to other bases. Moreover, choosing suitably the basis size, narrow resonances can be identified with one of the eigenstates of the Hamiltonian in the PS basis. Recently, we have extended this basis to describe systems with a valence+core structure (such as halo nuclei), taking into account the possible excitations of the core. This is the case of
^{11}
Be and odd-A carbon isotopes. We have applied this model to the
^{11}
Be+
^{208}
Pb reaction at 70MeV/u, where we found an improvement with respect to the single-particle model based on an inert core. The energy and angular distributions of the exclusive breakup for this reaction have been calculated using the Equivalent Photon Method, including both the E1 and E2 contributions. The calculated distributions are found to be in good agreement with the available experimental data from RIKEN. At the very forward angles, the cross section is completely dominated by the dipole couplings whereas we find a contribution of the quadrupole couplings, strongly influenced by the core excitations, at larger angles.
Friday, May 27, 2011 at 2:30 PM
Radioactive beams at RIBRAS: results and projects
Alinka Lépine-Szily
The only radioactive-beam facility in Brazil is located at the University of São Paulo. A 8MV tandem-Pelletron reaches energies of 3-5 MeV/nucleon for light nuclei. Since 2004, the RIBRAS (Radioactive Ion Beams Brasil) facility, made of two supraconductor solenoids, produces radioactive beams such as
^{6}
He,
^{7}
Be,
^{8}
B,
^{8}
Li,
^{10}
Be etc.
Recent results, as well as future projects at RIBRAS, are presented.
Monday, February 07, 2011 at 10:30 AM
The Impact of Exotic Reaction in Dense Stellar Matter
Mary BEARD
An interesting question in nuclear astrophysics is the fate of X-ray burst ashes as they descend under gravity to the deep layers of an accreting neutron star crust. As the ashes sink, they are subject to a range of nuclear reactions which transmute the nuclei. The primary of these reaction mechanisms are electron capture reactions, which are activated for different isotopes depending on the electron Fermi energy. At sufficiently high mass densities (rho =2.1×10
^{-9}
g cm
^{3}
for
^{12}
C+
^{12}
C and rho = 3.2 ×10
^{12}
g cm
^{-3}
for
^{40}
Mg +
^{40}
Mg), exotic density induced fusion reactions, known as pycnonuclear reactions, begin to occur. By combining existing electron capture formalism and a phenomenological expression for pycnonuclear reactions (specifically developed for a multi component plasma environment) with a network solver, the impact of pycnonuclear reactions in the neutron star crust is explored.
Friday, December 10, 2010 at 11:00 AM
"Einstein was wrong?" --EPR paradox and a test of Bell inequality by proton pairs
Dr. Hideyuki SAKAI
We have carried out the spin-correlation measurement of two protons in a spin singlet state aiming to test the EPR paradox presented by Einstein, Podolsky and Rosen in 1935. The EPR proposed a thought experiment in which they showed according to quantum mechanics that the result of a measurement of an entangled quantum system performed on earth, for example, can instantaneously influence the result of a measurement performed on the far distant Galaxy regardless of the distance. This of course contradicts with the theory of special relativity by Einstein, no information can be transmitted faster than the speed of light. Therefore EPR argued that quantum mechanics must be incomplete. In 1964, Bell found an extremely important inequality which is the embodiment of the EPR arguments. The prediction of the spin-correlation by the Bell's inequality is different from that by the quantum mechanics so that we can test experimentally which assertion is right by the measurement. After a short introduction of the EPR paradox, I try to explain how we realized an almost pure spin singlet state of two protons experimentally and how we measured the spin polarizations of two protons.
Wednesday, December 08, 2010 at 2:30 PM
On the connection between the nuclear vertex constant (the asymptotic normalization coefficient) for the virtual decay B ->A+a and the effective-range expansion parameters
R. Yarmukhamedov
The explicit expression for the nuclear vertex constant (NVC) (or respective asymptotic normalization coefficient (ANC)) for the virtual decay B-> A+a at an arbitrary orbital momentum l and the corresponding connection equation for the bound (A+a) state, which are valid both for the neutral case and for the charged case, are derived for the standard effective-range expansion K
_{l}
(k
^{2}
) restricting by terms up to k
^{6}
. Combining this expression and the bound state condition with the standard effective-range function makes it possible to reduce the number of the free effective range parameters on two if the “experimental” ANC-value is known. The new experimental values for the scattering length, effective range and parameter form are determined in this way for the
^{16}
O + p, α + t and α +
^{3}
He collisions by using the available corresponding “experimental” ANC. It is shown that the effective-range expansion for these collisions is valid up to energies larger 5 MeV. Comparison of these results with those recommended in work of R. Kamouni, D. Baye [Nucl.Phys. A 791 (2007) 86] is done.
Monday, November 15, 2010 at 2:00 PM
Foundation of CDCC and its recent development
YAHIRO Masanobu
1) History of CDCC.
2) Foundation of CDCC.
3) Recent development in CDCC.
Part (1): CDCC is a method for treating the three-body scattering with high accuracy. It was first proposed as a method of treating the deuteron breakup effect on deuteron elastic scattering and (d,p) reactions. At that time, the modelspace of the breakup process was not large enough. Kyushu group showed that the S-matrix element of CDCC converges as the modelspace of the breakup process is extended, and then applied it for breakup reactions themselves. The CDCC with the large modelspace was successful in reproducing experimental data on various kinds of three-body reactions.
Part 2): After the success of CDCC, the method was criticized for the foundation. The relation between CDCC and the Faddeev theory was not clear. This problem was solved by Austern, Yahiro and Kawai. Following the work, I explain the essence of CDCC. Very recently, CDCC solution was compared with Faddeev solution directly by Portuguese group. I also introduce this work.
Part 3): As a recent development of CDCC, I introduce four-body CDCC. This is a reaction theory for treating the four-body scattering. First of all, I show the effect of the four-body breakup process on the
^{6}
He elastic scattering. The effect is essential to reproduce the data on the scattering. In general, CDCC yields the breakup cross section as a discrete function of the excitation energy of projectile, but it should be a smooth function. A method for solving this problem is proposed. Four-body CDCC with this smoothing procedure is applied to (
^{6}
He,
^{ 4}
He n n) reaction with success in reproducing the data.
Tuesday, October 19, 2010 at 11:00 AM
Extensions rationnelles solubles des potentiels invariants de forme de seconde catégorie
Y. GRANDATI
Les potentiels invariants de forme primaires peuvent être classés en deux catégories équivalentes aux deux classes de Barclay-Maxwell. On montre que pour tous les potentiels appartenant à chacune de ces catégories, les dérivées logarithmiques des fonctions propres associées aux états liés peuvent s’exprimer sous forme de fractions continues finies en une variable appropriée. A chaque potentiel de la seconde catégorie, il est possible d’associer une famille infinie de potentiels rationnels en cette variable, réguliers et isospectraux au potentiel primaire considéré. Ces familles sont générées de façon directe, en appliquant un schéma de partenariat supersymétrique basé sur les états excités, combiné à des transformations d’invariance spécifiques à la seconde catégorie. Les potentiels ainsi obtenus ne sont autres que les potentiels associés aux polynômes orthogonaux exceptionnels de Laguerre et Jacobi.
Tuesday, April 13, 2010 at 11:00 AM
Description of few-particle systems using Faddeev-Yakubovski equations
Rimantas LAZAUSKAS
Finding exact solutions for the Quantum Mechanics problems starting from the Hamiltonian for interacting particles (so-called ab-initio calculations) presents a fundamental interest. With rare exceptions exact treatment of the problem one is limited to relatively simple systems ( "Few-Body"), nevertheless this knowledge allows us to judge on the relevance of interactions as well as allows to discover unexpected properties. The very general formalism that we use to solve Quantum Mechanics problems, namely Faddeev Yakubovski equations in configuration space, allows us to study in a consistent and rigorous way very different physical phenomenon: bound and resonant states, elastic and in-elastic scattering as well as Break-up process. In this seminar, the results of the numerical study of non-relativistic quantum three and four particle systems will be presented. Special attention will be given to the few nucleon systems, pointing out existent discrepancies in the realistic nucleon-nucleon interaction models.
Wednesday, March 25, 2009 at 2:30 PM
A microscopic cluster model study of the 3He+p scatterings
Koji Arai
We calculate the
^{3}
He+p scattering in two microscpic cluster models. One is the conventional calculation which employs the effective n-n potenatial(Minnesota) and a simple S-wave wave function as the cluster intrinsic function. Anonther is the extended calculation which employs the relastic N-N potential(G3RS) and the more complicated cluster intrionsic function. A comparison between these two calculations shows that the tensor force in the cluster internal motion make a substantial differece for the role of the addtional d+2p channel in the resonance states.
Wednesday, February 18, 2009 at 11:00 AM
Resonances and Continua in Three-Body Systems
Kiyoshi KATO
What is a resonant state ? Although there is no problem in two-body systems, it is not easy to solve resonant states in three-body systems. Berggren discussed the resonant state as a family member of bound states. His definition of resonant states is that they are complex energy eigenstates of the Hamiltonian with an outgoing boundary condition. This definition can be easily applied to three-body and general many-body systems. By using the complex scaling method, resonances and continua of three-body systems are solved in the same way as the bound- state calculations. Several examples of application of this method to nuclear cluster and two-neutron halo systems are presented.
Monday, February 02, 2009 at 2:30 PM
A new continuous family of two-dimensional exactly-solvable and (super)integrable Schroedinger equations
Alexander TURBINER
It is shown that the Smorodinsky-Winternitz potential, BC
_{2}
rational model, 3-body Calogero model, Wolves potential (G
_{2}
-rational model) are the members of a continuous family of two-dimensional exactly-solvable and (super)integrable Schroedinger equations marked by some continuous parameter. Their spectra is always linear in quantum numbers. Hidden algebra of the family for integer values of the parameter is uncovered. It is non-semi-simple Lie algebra gl(2) x R
^{k+1}
.
Wednesday, January 21, 2009 at 11:00 AM
Excitations and electro-weak transitions in
^{4}
He
W. HORIUCHI
I will discuss the structure of the excited states of
^{4}
He and electro-weak transitions from the ground state to the excited states. The wave functions are obtained accurately in a superposition of correlated bases using realistic interactions. All the levels below 26 MeV are reproduced well in the four-body calculation. I will show the three lowest-lying excited states have
^{3}
N+N(
^{3}
H+p,
^{3}
He+n) cluster structure.
In the final stage of a core collapse supernova, neutrinos are emitted from the collapsed core. It is important to evaluate a neutrino-nucleus reaction rate, namely weak transition rates from the ground state of
^{4}
He to the excited states.
Monday, June 30, 2008 at 11:00 AM
Inversion doublet of 3N+N cluster structure in excited states of
^{4}
He
Y. Suzuki
As a preparatory work for "Correlations and clustering in Core+few-nucleons model", we have studied the structure of
^{4}
He excited states in four-body calculations using realistic potentials. The aim is to describe the coexisting spectra of particle-hole and cluster excitations in a single scheme. The three lowest negative-parity states of
^{4}
He are understood as negative-parity partners of the first excited 0
^{+}
state which has 3N+N cluster structure.
Tuesday, June 10, 2008 at 11:00 AM
Non-empirical pairing energy functional for nuclei
T. DUGUET
I will discuss the first systematic finite-nuclei calculations performed using the Energy Density Functional method and a non-empirical pairing functional derived from basic nuclear interactions. The aim of such a work is two-fold
(i) improving on currently used empirical energy functionals that lack predictive power away from known experimental data
(ii) understand the microscopic processes responsible for superfluidity in finite nuclei.
Results of calculations performed at lowest-order in the nuclear plus Coulomb two-nucleon interactions will be presented and compared to experimental data. Doing so, neutron-neutron and proton-proton pairing properties of finite nuclei will be characterized in a systematic and microscopic way.
Monday, May 19, 2008 at 2:30 PM
The interaction between a nucleon and the 3-α system
A.TOHSAKI-SUZUKI
We present how to treat the interaction of a nucleon and N-α system which is described by a microscopic wave function responsible for the α condensation. The idea is based on the resonating group method. As our first target, we take the sytem of nucleon+3-α, that is,
^{13}
C and
^{13}
N. Especially, we focus upon the behaviour of the excited state of
^{12}
C as a nucleon comes in it.
Monday, May 19, 2008 at 11:00 AM
Internal density matrix for Bose-Einstein condensates with finite number of particles in a harmonic trap
H. HORIUCHI
We discuss the internal one-particle density matrix for Bose-Einstein condensates with finite number of particles in a harmonic trap. The internal one-particle density matrix is different for different choices of internal coordinates. The Pethick-Pitaevskii (PP)-type internal density matrix, whose eigenvalue problem is analytically solved, yields a fragmented condensate even in the limit of an infinite number of particles, while the Jacobi-type internal density matrix leads to an ideal condensate. In the macroscopic limit the internal density matrix should have the same eigenvalues and eigenfunctions as those of the corresponding ideal Bose-Einstein condensate in the laboratory frame, this being a very physical condition. Discussions are given on comparisons of Jacobi coordinates and the coordinates adopted by PP, where the former constitutes an orthogonal coordinate system but the latter does not.
Wednesday, April 30, 2008 at 11:00 AM
About the ground state of quartic oscillator
Alexander TURBINER
Quartic oscillator H = -d
^{2}
/dx
^{2}
+ ax
^{2}
+ x
^{4}
, with real a and x is one of the basic problems of quantum mechanics. A simple function which approximates uniformly the lowest eigenfunction with relative accuracy ≤ 10
^{-6}
for any x real at any |a| ≤ 20 is presented. The lowest eigenvalue found variationally with this function taked as trial provides 9 - 10 significant digits for any -20 ≤ a ≤ 20. A possible connection to recent remarkable result by Eremenko-Gabrielov-Shapiro about complex zeroes of eigenfunctions is mentioned. A comparison with one-instanton results is given.
Wednesday, April 16, 2008 at 11:00 AM
Coulomb Systems in a Strong Magnetic Field and Atmosphere of a Neutron Star
Alexander TURBINER
At 2002 the data collected by CHANDRA X-ray observatory led to a discovery of two absorption features in the spectra of radiation at 0.7 and 1.4 KeV (they were later confirmed by XMM-Newton) of the isolated neutron star 1E1027.4-5209 characterized by enormous surface magnetic field B > 10
^{12}
G. A natural question about a content of the neutron star atmosphere occurs. Following the old ideas of Mal Ruderman it can consist of atomic-molecular type compounds.
Atomic and molecular physics can be changed dramatically by a presence of a strong magnetic field. A complete classification of one- and two-electron Coulomb systems made from protons and/or α-particles which can exist at B < 10
^{16}
G is presented in BO approximation. It is demonstrated that in a magnetic field B > B
_{cr}
~ 10
^{11}
G traditional one-electron molecular systems like the H
_{2}
^{+}
molecular ion can cease to exist but exotic ones H
_{3}
^{2+}
(pppe), H
_{4}
^{3+}
(ppppe), even H
_{5}
^{4+}
(pppppe) and He
_{2}
^{3+}
(α α e), (HeH)
^{2+}
(α pe) can occur (!). It turns out the neutral hydrogen atom is the least bound one-electron system in a magnetic field and the ion H
_{4}
^{+++}
is the most bound at the highest magnetic fields. For two-electron molecular systems H
_{2}
, H
_{3}
^{+}
, He
_{2}
^{2+}
, HeH
^{+}
, He
_{3}
^{4+}
oriented along a magnetic line an unusual phenomenon appears: the quantum numbers of the lowest energy state depend on a magnitude of the magnetic field and evolve from
^{1}
Σ
_{g}
at B < 10
^{8}
G to
^{3}
Σ
_{u}
and, eventually, to the strongly-bound
^{3}
Π
_{u}
. For all 2e systems the
^{3}
Σ
_{u}
state is the repulsive or weakly bound state and the corresponding system may not exist. E.g. the ion He
_{2}
^{2+}
does not exist at 10
^{8}
< B < 10
^{12}
G.
In general, studies in a strong magnetic are extremely complicated technically. Novel variational approach to the few-electron Coulomb systems based on physically relevant trial functions turns to be very successful, it provides highly accurate results. The approach allows to overcome significantly the classical results by James-Coolidge for H
_{2}
-molecule with few-parametric trial function. A unique, state-of-the-art numerical multidimensional integration routine is developed.
It is argued that the atmosphere of the neutron star 1E1027.4-5209 with surface temperature ≈ 10
^{6}
K may consist of a mixture of the exotic molecular ions H
_{3}
^{++}
and He
_{2}
^{3+}
at magnetic field ~ 10
^{13}
G.
Wednesday, February 27, 2008 at 11:00 AM
ALPHA-PARTICLE CONDENSATION IN NUCLEAR SYSTEMS
Peter SCHUCK
We first show how the onset of alpha-particle condensation in infinite nuclear matter can be treated and put into evidence at low densities. The analogous situation in n-alpha nuclei is given by low density states close to the n-alpha disintegration threshold, where alpha-particles move almost independently in relative 0S-states, hold together only by the Coulomb barrier. One of these states is the fameous Hoyle state of astrophysics, i.e. the 0
_{2}
^{+}
state at 7.65 MeV in
^{12}
C. All past and more recent studies unambiguously show that this state has very low density (about 1/3 of saturation density) and that it can be described to good approximation as a product state of three alpha-particles where the alphas, with respect to their c.o.m. motion, are all condensed into the 0S-orbit. The theoretical investigations show that analogous states should also exist in 16O, 20 Ne, 24Mg, etc. For example the 0+ state at 15.1 MeV in 16O seems to be identified as a strong candidate for a four alpha-particle condensed state. The possibility of alpha-particle condensation in heavier nuclei and in the astrophysical context will also be discussed.
Monday, February 18, 2008 at 11:00 AM
The Invisible Quantum Barrier
Mahir HUSSEIN
We construct the quantum barrier which represents the phenomenon of quantum reflection using the available data on single sodium atom and Bose-Einstein Condensate reflection from a solid silicon surface.The interaction between the atoms and the surface is the attractive Casimir-Polder potential. Thus the reflection is classically forbidden. We use the Abel equation to invert the data. We deduce this "invisible" barrier for the cases of atom and BEC reflection from the silicon surface. The resulting invisible quantum barrier is double-valued in both axes. A time-dependent, one-spatial dimension Gross-Pitaevskii equation is solved for the BEC case. We found that the BEC behaves very similarly to the single atom except for size effects, which manifest themselves in a maximum in the reflectivity at small distances from the wall. The effect of the atom-atom interaction on the reflection and correspondingly on the invisible barrier is found to be small.
Wednesday, December 12, 2007 at 2:00 PM
DYNAMICS OF MACROSCOPIC AND MICROSCOPIC THREE-BODY SYSTEMS
Yasuyuki SUZUKI
I would like to focus on some problems of three-body systems which arise when the constituent particles are composite, particularly those arising from the Pauli principle and the non-locality of the interaction between the particles. First, in order to show the power of the three-body approach I will present our recent application to a Borromean
^{20}
C+ n+n system for the structure study of
^{22}
C. The three-body dynamics is treated in a macroscopic approach where 20C is assumed to be an inert core but the valence neutrons are restricted to be orthogonal to the orbits occupied in the 20C core. This study leads to the conclusion that 22C is an S-wave two-neutron halo nucleus. In the above example, we have no Pauli-forbidden states between the two neutrons. It is interesting to ask a question: What happens if we have forbidden states between all pairs of the particles.
As a good example of this case, I will discuss a 12C nucleus as a system of three alpha-particles interacting via either a shallow L-dependent potential or a deep L-independent potential. I will point out that the definition of the Pauli-forbidden states plays a crucial role in the macroscopic approach of this system, and compare it with a calculation using an interaction which is derived from two-α resonating group method kernel. Finally, I will present our result of calculation for the triton binding energy which is obtained using the nucleon-nucleon interaction derived from a quark model for octet baryons. The nucleon-nucleon potential based on the spin-flavour SU(6) quark model reproduces experimental phase shifts equally well as modern realistic potentials. The quark-model potential is non-local and energy-dependent, so some care is needed to solve the three-body dynamics. It appears that our model gains more energy than those which use the latter potentials. This result may have an important consequence for determining the strength of three-body forces in nuclei.
Tuesday, September 11, 2007 at 4:30 PM
REACTION CROSS SECTION AND STRUCTURE OF CARBON ISOTOPES
W. HORIUCHI
I would like to focus on some problems of three-body systems which arise when the constituent particles are composite, particularly those arising from the Pauli principle
Tuesday, April 04, 2006 at 3:00 PM
t+t clustering in He-isotopes
Dr. Shigeyoshi Aoyama
^{6}
He has been studied by many authors, because it is expected to be most simple nucleus which has a halo structure. Since 4He is very stable, they have employed the 4He+n+n three-body model. However, they can not explain the binding energy of the ground state. Csoto numerically proved the reason as the importance of the t+t component even for the ground state. Therefore, even for the 6He nucleus, which is naturally expected to be having a shell model-like structure, we must consider the cluster components such as t+t. Recently, we have systematically investigated t+t components in He-isotopes. And, we understand that t+t components are also important for other neutron-rich He-isotopes.
Contact person: P. Descouvemont - pdesc@ulb.ac.be
Last updated July 28, 2009