Session 12
Applications in Particle and Nuclear Physics
Chairs:
Piet Van Isacker (Grand Accelerateur National dIons Lourds, France)
Yu-Min Zhao (Shanghai Jiaotong University, China)
Titles and Abstracts
Joseph N. Ginocchio (Los Alamos National Laboratory, USA)
Title: Relativistic symmetries in Nuclei and Hadrons
Abstract: Quasi-degenerate “pseudospin” doublets were discovered many years ago
in both spherical and deformed nuclei [1-5]. We show that pseudospin symmetry is an
SU(2) symmetry of the Dirac Hamiltonian which occurs when the scalar and vector
potentials are opposite in sign but equal in magnitude [6,7]. This symmetry occurs
independent of the shape of the nucleus: spherical, axial deformed, triaxial, and
gamma unstable.
We survey the evidence that pseudospin symmetry is approximately conserved for a
Dirac Hamiltonian with realistic scalar and vector potentials by examining the energy
spectra, the lower components of the Dirac eigenfunctions, the magnetic dipole and
Gamow-Teller transitions in nuclei, the upper components of the Dirac eigenfunctions,
and nucleon –nucleus scattering [8-14].
We shall also search for a fundamental rationale for pseudospin symmetry in terms of
chiral symmetry breaking as suggested by QCD sum rules [15]. A starting point is an
investigation of pseudospin breaking in the nucleon-nucleon interaction by studying
nucleon-nucleon scattering as a function of energy [16].
Furthermore we show that spin symmetry is an SU(2) symmetry of the Dirac
Hamiltonian which occurs when the scalar and vector potentials are equal in
magnitude. We show that heavy mesons and anti-nucleons in a nuclear environment
have spin symmetry.
We then show that the relativistic harmonic oscillator with spin symmetry has an U(3)
symmetry and that the relativistic harmonic oscillator with pseudospin symmetry has
a pseudo-U(3) symmetry and we derive the generators for both limits [17].
[1] A. Arima, M. Harvey and K. Shimizu, Phys. Lett. B 30, 517 (1969).
[2] K.T. Hecht and A. Adler, Nucl. Phys. A 137, 129 (1969).
[3] A. Bohr, I. Hamamoto and B. R. Mottelson, Phys. Scr. 26 267 (1982).
[4] D. Troltenier, W. Nazarewicz, Z. Szymanski, and J. P. Draayer, Nucl. Phys. A567
(1994) 591.
[5] F. S. Stephens et al, Phys. Rev. C 57, R1565 (1998).
[6] J. N. Ginocchio, Phys. Rev. Lett. 78, 436 (1997).
[7] J. N. Ginocchio and A. Leviatan, Phys. Lett. B 425, 1 (1998).
[8] J. N. Ginocchio and D. G. Madland, Phys. Rev. C 57, 1167 (1998).
[9] J. N. Ginocchio, Phys. Rev. C59, 2487 (1999).
[10] P. von Neumann-Cosel and J. N. Ginocchio, Phys. Rev. C62, 014308 (2000).
[11] J. N. Ginocchio and A. Leviatan, Phys. Rev. Lett. 87, 072502 (2001).
[12] B. Bowlin, A. S. Goldhaber, and C. Wilkin, Zeitschrift fur Physik A 331, 83
(1988).
[13] J. N. Ginocchio, Phys. Rev. Lett. 82, 4599 (1999).
[14] H. Leeb and S. Wilmsen, Phys. Rev. C62, 024602 (2000).
[15] T. D. Cohen, R. J. Furnstahl, K. Griegel, and X. Jin, Prog. in Part. and Nucl. Phys.
35, 221 (1995).
[16] J. N. Ginocchio, Physical Review C65, 054002 (2002).
[17] Joseph N. Ginocchio, Phys. Rev. Lett. 95, 252501 (2005).
Yu-Xin Liu (Peking University, China)
Title: Some Fundamental Aspects of Many Particle Systems in Group Theoretical
Approach
Abstract: The system composed of many particles each of which has angular
momentum ji holds the symmetry U ( (2 ji  1)) . The possible total angular
i
momenta of the system and their multiplicities, the values of the interaction matrix
elements, and the criterion to check the correctness of the computational code
evaluating the eigenvalue problem are the fundamental aspects in studying the
properties of the system. Basing on the Lie group representation theory, we have
given a simple recursion formula to get all the multiplicities of the total angular
momenta and an explicit expression for the d-boson system. To get the one-body and
two-body interaction matrix elements of the system with any possible seniority and
total angular momentum, one needs the isoscalar factors (ISF) of the reductions
U ( N )  O( N ) , U ( N )  SP( N ) , O ( N )  O (3) and SP( N )  O(3) . We have also
given the recursion formulae and the computational codes to get the matrix elements.
As for checking the correctness of the code to evaluate the eigenvalues, we have
developed a group chain approach based on the general principle of symmetry of a
system.
Yanan Luo (Nankai University, China)
Title: SD-pair shell model for even-even system
Abstract: The SD-pair shell model (SDPSM) is shown to reproduce approximately
typical spectra, E2 transition strengths of the U(5), SO(6), SU(3) and SU^*(3) limits
of the interacting boson model (IBM). The shape phase transitional patterns of the
IBM can also be reproduced in the SDPSM. As an example, the experimental data
for Xe and Ba isotopes are studied and the results show that the SDPSM can produce
the experiments very well. This analysis confirms that the IBM has a sound
shell-model foundation; it also demonstrates that the truncation scheme adopted in the
SDPSM is reasonable.
Feng Pan (Liaoning Normal University, China)
Title: The Heine-Stieltjes correspondence and the polynomial approach to the SU(2)
Gaudin-Richardson models
Abstract: The Heine-Stieltjes correspondence is extended to the cases corresponding
to the Bethe ansatz equations of the SU(2) Gaudin-Richardson models, with which a
new polynomial approach to exact solutions of such quantum many-body problems is
established. As examples of the application, the extended Heine-Stieltjes polynomials
resulting from the solution of the two-site Bose-Hubbard model and those for the
standard nuclear pairing model are discussed. The new approach may be used to
search for exact solutions of a large class of quantum many-body problems and to
establish a new angular momentum projection technique.
Jialun Ping (Nanjing Normal University, China)
Title: The group theoretic method in the multi-quark system study
Abstract: A group theoretic method for the systematic study of multiquark states is
developed. The calculation of matrix elements of many-body Hamiltonians is
simplified by transforming the physical bases (quark cluster bases) to symmetry bases
(group chain classified bases), where the fractional parentage expansion method can
be used. Five- and six-quark systems are taken as the example in this study. Three
quark models are used to show the general applicability of the new multiquark
calculation method and general results of constituent quark models for five- and
six-quark states are given.
Chong Qi (Royal Institute of Technology, Sweden)
Title: Analytic study of the partial seniority conservation
Abstract: A partial conservation of the seniority quantum number in j = 9/2 shells has
been found recently in a numerical application. In this contribution I will present an
analytic proof for this problem. I will analyze the properties of the non-diagonal
matrix elements with the help of the one-particle and two-particle coefficients of
fractional parentage (cfp's). It is found that all non-diagonal (and the relevant diagonal)
matrix elements can be re-expressed in closed forms and are proportional to certain
one-particle cfp's. This remarkable occurrence of partial dynamic symmetry is the
consequence of the peculiar property of the j = 9/2 shell, where all v = 3 and 5 states
are uniquely defined.
Fan Wang (CPNPC, Nanjing University and CAS, China)
Title: Group representation versus Quantum representation and a New approach to
group representation calculations
Abstract: We developed a group representation theory and calculation method based
on quantum representation theory. All the calculations, such as Character, Irreducible
bases and Matrices, Projection operators, Clebsch-gordan series and coefficients are
reduced to solve a set of eigan-equations of a complete set of commuting operators
consisting of the class operators of the group. This approach had been successfully
applied to all of the finite groups and compact Lie groups and various useful
coefficients for physical application of group representation theory had been
calculated and tabulated.
Feng-Shou Zhang (Beijing Normal University, China)
Title: Effects of symmetry and shell structure in heavy ion fusion reactions
Abstract: The magic numbers were successfully explained by the nuclear shell model
proposed by Gopper-Mayer and Jensen sixty years ago. The shell model predicts that
the next doubly magic nucleus in the sequence will contain either 114, 120, 124 or
126 protons and 184 neutrons. However, the dynamical process of the formation of
superheavy nucleus is not understood well enough. In this work, by using an
improved isospin dependent molecular dynamics model in which the shell correction
energy of the system is calculated by using deformed two-center shell model and the
surface energy of the system is improved by introducing a switch function that
combines the surface energies of projectile and target with the one of the compound
nucleus, the effects of the shell correction energy on synthesis of superheavy nuclei
and the fusion cross sections in asymmetric and nearly symmetric reaction systems
leading to the same compound nuclei are studied. The entrance channel mass
asymmetry dependence of compound nucleus formation is found by analyzing the
shell correction energies, Coulomb barriers and fusion cross sections. The calculated
results are in agreement with the experimental data and it is found that the compound
nucleus formation is favorable for the systems with larger mass asymmetry.
Yu-Min Zhao (Shanghai Jiaotong University, China)
Title: The SO(3) symmetry for a single-j shell and the Pauli principle
Abstract: In the nuclear shell model, number of states with given total angular
momentum and angular momentum coupling coefficients are fundamental practices. I
would like to present some analytical formulas of the dimension of a single-j shell,
many new sum rules of angular momentum coupling coefficients for a single-j shell,
as well as their relations via the Pauli principle.