Pairing effect in many-nucleon system

The method of coherent correlated pairs is applied with a realistic effective Hamiltonian to the four-nucleon system. Three methods of solution are compared for ease of implementation and convergence rates. A Monte Carlo method yields the best upper bound within the coherent correlated pair space. The full variational treatment of the four-nucleon coherent correlated pair problem yields equations which have poor stability properties. An ansatz variational method proves to be rapidly convergent and yields results very close to those of the Monte Carlo method. The results for binding energy and the one body density distribution are compared with Hartree-Fock results using the same effective Hamiltonian in the same model space. As in previous soluble model applications the coherent correlated pair method provides a superior upper bound to the ground state energy.The method of coherent correlated pairs is applied with a realistic effective Hamiltonian to the four-nucleon system. Three methods of solution are compared for ease of implementation and convergence rates. A Monte Carlo method yields the best upper bound within the coherent correlated pair space. The full variational treatment of the four-nucleon coherent correlated pair problem yields equations which have poor stability properties. An ansatz variational method proves to be rapidly convergent and yields results very close to those of the Monte Carlo method. The results for binding energy and the one body density distribution are compared with Hartree-Fock results using the same effective Hamiltonian in the same model space. As in previous soluble model applications the coherent correlated pair method provides a superior upper bound to the ground state energy.

Physical Review CMar 1, 19846 citations

Shannon entropy of optimized proton-neutron pair condensates

Shu-Yuan Liang, Yi Lu, Yang Lei +3 more

Proton-neutron pairing and like-nucleon pairing are two different facets of atomic nuclear configurations. While like-nucleon pair condensates manifest their superfluidic nature in semimagic nuclei, it is not absolutely clear if there exists a $T=0$ proton-neutron pair condensate phase in $N=Z$ nuclei. With an explicit formalism of general pair condensate with good particle numbers, we optimize proton-neutron pair condensates for all $N=Z$ nuclei between $^{16}\mathrm{O}$ and $^{100}\mathrm{Sn}$ , given shell model effective interactions. As comparison, we also optimize like-nucleon pair condensates for their semimagic isotones. Shannon entanglement entropy is a measurement of mixing among pair configurations, and can signal intrinsic phase transition. It turns out the like-nucleon pair condensates for semimagic nuclei have large entropies signaling an entangled phase, but the proton-neutron pair condensates end up not far from a Hartree-Fock solution with small entropy. With artificial pairing interaction strengths, we show that the general proton-neutron pair condensate can transit from an entangled $T=1$ phase to an entangled $T=0$ phase, i.e., pairing phase transition driven by external parameters. In the $T=0$ limit, the proton-neutron pair condensate optimized for $^{24}\mathrm{Mg}$ turns out to be a purely $T=0$ P-pair condensate with large entanglement entropy, although such cases may occur in cold atom systems, unlikely in atomic nuclei.Proton-neutron pairing and like-nucleon pairing are two different facets of atomic nuclear configurations. While like-nucleon pair condensates manifest their superfluidic nature in semimagic nuclei, it is not absolutely clear if there exists a $T=0$ proton-neutron pair condensate phase in $N=Z$ nuclei. With an explicit formalism of general pair condensate with good particle numbers, we optimize proton-neutron pair condensates for all $N=Z$ nuclei between $^{16}\mathrm{O}$ and $^{100}\mathrm{Sn}$, given shell model effective interactions. As comparison, we also optimize like-nucleon pair condensates for their semimagic isotones. Shannon entanglement entropy is a measurement of mixing among pair configurations, and can signal intrinsic phase transition. It turns out the like-nucleon pair condensates for semimagic nuclei have large entropies signaling an entangled phase, but the proton-neutron pair condensates end up not far from a Hartree-Fock solution with small entropy. With artificial pairing interaction strengths, we show that the general proton-neutron pair condensate can transit from an entangled $T=1$ phase to an entangled $T=0$ phase, i.e., pairing phase transition driven by external parameters. In the $T=0$ limit, the proton-neutron pair condensate optimized for $^{24}\mathrm{Mg}$ turns out to be a purely $T=0$ P-pair condensate with large entanglement entropy, although such cases may occur in cold atom systems, unlikely in atomic nuclei.

arXiv:2411.01439Physical Review CFeb 13, 20258 citations

MANY-BODY EFFECTS AND PAIRING CORRELATIONS IN FINITE NUCLEI

E. Vigezzi, P. F. Bortignon, G. Colò +4 more

International Spring Seminar on Nuclear PhysicsMar 1, 20050 citations

T=0

proton-neutron pair condensate phase in

N=Z

nuclei. With an explicit formalism of general pair condensate with good particle numbers, we optimize proton-neutron pair condensates for all

N=Z

nuclei between

^{16}\mathrm{O}

and

^{100}\mathrm{Sn}

, given shell model effective interactions. As comparison, we also optimize like-nucleon pair condensates for their semimagic isotones. Shannon entanglement entropy is a measurement of mixing among pair configurations, and can signal intrinsic phase transition. It turns out the like-nucleon pair condensates for semimagic nuclei have large entropies signaling an entangled phase, but the proton-neutron pair condensates end up not far from a Hartree-Fock solution with small entropy. With artificial pairing interaction strengths, we show that the general proton-neutron pair condensate can transit from an entangled

T=1

phase to an entangled

T=0

phase, i.e., pairing phase transition driven by external parameters. In the

T=0

limit, the proton-neutron pair condensate optimized for

^{24}\mathrm{Mg}

turns out to be a purely

T=0

P-pair condensate with large entanglement entropy, although such cases may occur in cold atom systems, unlikely in atomic nuclei.