# Bulletin of the American Physical Society

## 2005 2nd Joint Meeting of the Nuclear Physics Divisions of the APS and The Physical Society of Japan

Sunday–Thursday, September 18–22, 2005; Maui, Hawaii

### Session KK: Nuclear Theory III

Sponsoring Units: DNP JPS
Chair: Thomas Luu, Los Alamos National Laboratory
Room: Ritz-Carlton Hotel Maui

Thursday, September 22, 2005 			   2:00PM -  2:15PM  KK.00001: Critical Point Symmetry in A Fermion Monopole and Quadrupole Pairing Model 			 			 	   Joseph N. Ginocchio 	  Recent interest in symmetries at a critical point of phase transitions in  nuclei prompts a revisit to the fermion monopole and quadrupole   pairing model [1]. This model has an exactly solvable symmetry limit that is  transitional between spherical nuclei and gamma unstable deformed nuclei.  The eigenenergies, eigenfunctions, pairing strength and quadrupole  transition rates in this limit are derived. Comparison with empirical  quadrupole transition rates suggests that the Xenon isotopes may have this  symmetry [2].  1. Joseph N. Ginocchio, Ann. Phys. 126, 234 (1980).  2. Joseph N. Ginocchio, Phys. Rev. C (2005).
Thursday, September 22, 2005 			   2:15PM -  2:30PM  KK.00002: All-order core polarization for shell-model effective interactions 			 			 	   Jason D. Holt 	   	  , Jeremy Holt 	   	  , T.T.S. Kuo 	   	  , G.E. Brown 	   	  , Scott Bogner 	  Although core polarization, calculated to second-order in perturbation  theory, has been successful in describing a range of nuclear  observables, the effect of high-order diagrams has been a  long-standing issue.  In this talk we present an all-order summation of  a large class of core polarization diagrams using the low-momentum NN  interaction $V_{low-k}$.  Our calculation, based on the elegant formalism  of Kirson and Babu-Brown, involves solving a set of coupled non-linear  equations in which the vertex functions are generated self-consistently. By using $V_{low-k}$, which is energy independent, and true Green  functions in the particle-particle and particle-hole channels, we can  simplify the solution and include a class of diagrams whose calculation  has been previously intractable.  We apply this procedure to the  $sd$-shell effective interactions and find that the all-order calculation  serves to mildly suppress the second order results, typically by less  than 10\%.
Thursday, September 22, 2005 			   2:30PM -  2:45PM  KK.00003: Very-low Momentum Nucleon-Nucleon Interaction Based upon Chiral Perturbation Theory 			 			 	   Ruprecht Machleidt 	   	  , Luigi Coraggio 	   	  , David Entem 	  Recently, several groups have constructed low-momentuum nucleon-nucleon (NN) interactions that have become known as $V_{\rm low-k}$. One starts from a conventional high-momentum NN potential and applies renormalization group techniques that preserve the (half)-on-shell T-matrix to obtain a new potential that is charcterized by a low-momentum cutoff, typically around 2 fm$^{-1}$. The general justification for this proceedure comes from low-energy effective field theory (EFT). This fact suggests that there may be a more efficient way to construct a $V_{\rm low-k}$. Namely, instead of taking the detour through a high-momentum NN potential, one may as well construct a low-momentum potential from scratch---and this is what our contribution is about. We use chiral perturbation theory at next-to-next-to-next-to-leading order (N3LO) and apply a sharp cutoff at 2.1 fm$^{-1}$. This potential reproduces the NN phase shifts up to about 300 MeV lab energy and the deuteron properties. While the $V_{\rm low-k}$ constructed in the past allow only for a rather cumbersome numerical representation, our low-momentum potential is given in analytic form. Moreover, the low-energy constants are explicitly known such that the chiral three-nucleon forces consistent with our NN potential can be properly defined.
Thursday, September 22, 2005 			   2:45PM -  3:00PM  KK.00004: Fermi liquid theory and Kuo-Brown effective interactions 			 			 	   Jeremy W. Holt 	   	  , G.E. Brown 	   	  , J.D. Holt 	   	  , T.T.S. Kuo 	   	  , S.K. Bogner 	  We study the properties of nuclear matter using the           low-momentum nucleon-nucleon interaction $V_{\rm low-k}$ and  Landau's theory of normal Fermi liquids. The Landau           $f$-function, which describes the quasiparticle-quasihole  interaction at the Fermi surface, can be expanded in Legendre  polynomials whose coefficients are directly related to the  effective mass, symmetry energy, and compression modulus of  nuclear matter. It is found that in the single-bubble  approximation to the induced interaction of Babu and Brown, the  compression modulus is much too repulsive compared with  experiment. This is remedied by solving the Babu-Brown equation  self-consistently using $V_{\rm low-k}$ as the driving term.  The result is a reasonable agreement with experiment, both for  the compression modulus and the remaining Fermi liquid  parameters. In addition, we discuss the effect of high-order  direct and exchange terms in the quasiparticle scattering  amplitude.
Thursday, September 22, 2005 			   3:00PM -  3:15PM  KK.00005: Shell Model Analysis of the $^{56}$Ni Spectrum in the Full $pf$ Model Space 			 			 	   Mihai Horoi 	   	  , B. Alex Brown 	   	  , T. Otsuka 	   	  , M. Honma 	   	  , T. Mizusaki 	  We present a full $pf$-shell spectroscopy of the low-lying  states of $^{56}$Ni using the GXPF1A interaction.[M. Honma et al., Proceedings of ENAM,  2004]  Both, the ground state band and the first deformed band, as  well as the transition probabilities compares favorably with the  experimental data.[D. Rudolpf et al., Phys. Rev. Lett. {\bf 82},  5763 (1999)]  We analyze the significance of  the $np-nh$ contributions to the full model calculations,  similar to the analysis done for $^{28}$Si in the $sd$-shell some twenty years ago.[Brown and  Wildenthal, Ann. Rev. Nucl. Part. Sci. {\bf 38}, 29 (1988)]
Thursday, September 22, 2005 			   3:15PM -  3:30PM  KK.00006: Exactly Solvable Nuclear Models and Richardson-Gaudin Algebraic Structures 			 			 	   V.G. Gueorguiev 	   	  , J. Dukelsky 	   	  , P. Van Isacker 	   	  , S.S. Dimitrova 	  We discuss the exact solution of the isovector pairing (T=1) in nuclei within the  SO(5) Richardson-Gaudin model. $^{64}$Ge is used to illustrate the parameter  space and shed light on the  solutions of the Richardson-Gaudin models. Basic  properties of the integrable Richardson-Gaudin models are summarized and their  possible applications to variety of nuclear physics models are emphasized. This  work was partially performed under the auspices of the U. S. Department of Energy  by the University of California, Lawrence Livermore National Laboratory under  contract No. W-7405-Eng-48.
Thursday, September 22, 2005 			   3:30PM -  3:45PM  KK.00007: The Redmond Formula with Seniority 			 			 	   Larry Zamick 	   	  , Alberto Escuderos 	  As we get to heavier nuclei, we find more states with different seniorities and several states of a given seniority. There is a recursion formula  by Redmond that relates an $n \to (n+1)$ coefficient of fractional parentage (cfp) to that of $(n-1) \to n$. However, this involves an {\it overcomplete} set of  principal parent (pp) cfp's. For example, for a 3-particle system, we can form basis states $[ [12]^{J_0} 3]^J$, where $J_0$ is the pp; we then antisymmetrize and normalize $\Psi [J_0]=N[J_0] (1-P_{12}-P_{13}) \left[ [12]^{J_0} 3\right]^J$, and form a ppcfp expansion $\Psi[J_0]=\sum_{J_1} [j^2 (J_1) j |\} j^ 3 [J_0] J] \left[ [12]^{J_1} 3\right]^J$. But for, say, $J=j=9/2$, there are five $\Psi[J_0]$'s, but only two independent wave functions, one with seniority 1 and  one with seniority 3. We note that $[j^2 (J_0) j |\} j^3 [J_0] J]=1/(3 N[J_0])$. We are able then to obtain the following relation between overcomplete ppcfp's and complete orthonormal cfp's: $A=B=C$, where $$A=(n+1)[j^n(J_0 v_0) j |\} j^{n+1} [J_0 v_0] J] \; \; [j^n (J_1 v_1) j |\} j^{n+1} [J_0 v_0] J],$$ $$B=(n+1) \sum_v [j^n (J_0 v_0) j |\} j^{n+1} J v] \; \; [j^n (J_1 v_1) j |\} j^{n+1} J v],$$ $$C=\delta_{J_0 J_1} \delta_{v_0 v_1} + n (-1)^{J_0+J_1} \sqrt{(2J_0+1)(2J_1+1)} \sum_{v_2 J_2} \begin{Bmatrix} J_2 & j & J_1 \\ J & j & J_0 \end{Bmatrix} \times$$ $$\times [j^{n-1} (J_2 v_2) j |\} j^n J_0 v_0] \; \; [ j^{n-1} (J_2 v_2) j |\} j^n J_1 v_1].$$
Thursday, September 22, 2005 			   3:45PM -  4:00PM  KK.00008: Applications of RPA in the nuclear shell model 			 			 	   Calvin Johnson 	   	  , Ionel Stetcu 	  In recent work we have described a computational implementation of the random phase approximation (RPA) in the interacting  shell model. Such an implementation is computationally much  cheaper than full scale diagonalization, and provides a  reasonable approximation, to binding energies and transitions,  including charge-changing transitions. Here we discuss the  latest applications of our computer code, SHERPA, with an  emphasis on astrophysics.
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