Neutron-proton Pairing Research Articles

Ground-state properties of even-evenN=Znuclei within the Hartree-Fock-BCS and higher Tamm–Dancoff approaches

We calculate the ground-state properties of well deformed, even-even $N=Z$ nuclei in the region between $^{56}\mathrm{Ni}$ and $^{100}\mathrm{Sn}$ within two different approaches, focusing on the binding energy and deformation and pairing properties. First, we employ the Hartree-Fock-BCS (HFBCS) approximation with the Skyrme effective nucleon-nucleon interaction and discuss how the results depend on the parametrization of the interaction and on the pairing force parameters adjusted in various schemes to reproduce the experimental odd-even mass differences. Then, within the Higher Tamm-Dancoff Approximation (HTDA), which explicitly conserves the particle number, we calculate the same properties starting from the HFBCS solutions. The HTDA treatment of the ground-state correlations is converged within a $n$-particle-$n$-hole expansion using up to $n=4$ particle-hole excitations of the pair type (in the sense of Cooper pairs). We compare the ground-state properties calculated in these two descriptions of pairing correlations and deduce the importance of the particle-number conservation in weak pairing regimes. Finally, we extend the HTDA calculations so as to include the proton-neutron residual interaction and investigate the role of proton-neutron pairing on the above ground-state properties.

PAIRING OF STRONGLY CORRELATED NUCLEONS

Pairing properties of infinite matter are surveyed that are obtained from self-consistent Green's function calculations. A complete treatment of off-shell propagation that incorporates the effects of short-range correlations is included. Mean-field calculations based on the BCS approach are superseded by the present results, which resolve a long-standing puzzle associated with 3S1-3D1 (proton-neutron) pairing in symmetric nuclear matter. Results for 1S0 pairing in pure neutron matter are in agreement with recent Monte-Carlo calculations for this system. The possibility of proton pairing in finite nuclei, as a result of increasing proton correlations with increasing nucleon asymmetry, is pointed out.

Precision mass measurements of rare isotopes nearN=Z=33produced by fast beam fragmentation

Mass measurements of $^{63,64}\mathrm{Ga}$, $^{64,65,66}\mathrm{Ge}$, $^{66,67,68}\mathrm{As}$ and $^{69}\mathrm{Se}$ performed at the LEBIT facility at the NSCL by Penning trap mass spectrometry are presented. The rare isotopes were produced by fast beam fragmentation and in-flight separation, then converted to a low energy beam using a gas stopping technique. Masses of the $N=Z$ nuclei $^{66}\mathrm{As}$ and $^{64}\mathrm{Ge}$ have been determined with uncertainties of $\ensuremath{\delta}\mathrm{m}/\mathrm{m}=5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ and $6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$, respectively, representing a more than ten-fold improvement in precision over previous measurements. For $^{63,64}\mathrm{Ga}$, $^{65,66}\mathrm{Ge}$, $^{67,68}\mathrm{As}$, and $^{69}\mathrm{Se}$ relative mass uncertainties of $\ensuremath{\delta}\mathrm{m}/\mathrm{m}l5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ were obtained. $^{69}\mathrm{Se}$ is found to be 135 keV more bound than the value listed in the 2003 Atomic Mass Evaluation. Using theoretical Coulomb shift energies in combination with the experimental mass values for $^{65,66}\mathrm{Ge}$, $^{67}\mathrm{As}$, and $^{69}\mathrm{Se}$, masses for $^{65}\mathrm{As}$, $^{66,67}\mathrm{Se}$, and $^{69}\mathrm{Br}$ are predicted with an estimated uncertainty of 100 keV. These mass values, in conjunction with our measurements, were used to calculate improved effective lifetimes of the rp-process waiting point nuclei $^{64}\mathrm{Ge}$ and $^{68}\mathrm{Se}$. We find that $^{64}\mathrm{Ge}$ is less of a waiting point while $^{68}\mathrm{Se}$ poses a larger delay in the rp-process than previously thought. The improved mass values in this region were also used to investigate the neutron-proton pairing energy of odd-odd $N=Z$ nuclei.

PARTICLE NUMBER CONSERVING APPROACH TO CORRELATIONS

In the present work the so-called Higher Tamm-Dancoff Approximation method is presented for the generalized case of isovector and isoscalar residual interactions treated simultaneously. The role of different particle-hole excitations and of proton-neutron pairing correlations in the ground state of the self-conjugate 64 Ge nucleus is discussed.

40 YEARS OF THE DYNAMICAL PROTON-NEUTRON PAIRING SYMMETRIES

In the years 1964-66 several physicists from several groups were searching quite independently for new symmetries related to the proton-neutron pairing interaction. They exploited the so-called quasi-spin method introduced earlier to apply to the system of electrons and then to identical nucleons (only protons or only neutrons). In what follows, a short introduction to the quasi-spin method is presented and then its application to the pairing interaction of neutrons (protons) is given. With the help of the quasi-spin method, the orthogonal symmetry groups SO(5) and SO(8) are shown to deal with proton-neutron pairing interaction in j - j and L - S coupling schemes, respectively. Comments about chronology of published papers related to the symmetry of pairing interaction written by inventors of the new symmetries are also made.

RADII AND BINDING ENERGIES OF NUCLEI IN THE ALPHA-CLUSTER MODEL

The α-cluster model is based on two assumptions that the proton–neutron pair interactions are responsible for adherence between α-clusters and that the NN-interaction in the α-clusters is isospin independent. It allows one to estimate the Coulomb energy and the short range inter-cluster bond energy in dependence on the number of clusters. The charge radii are calculated from the number of α-clusters too. Unlike the Weizsäcker formula in this model the binding energies of alpha-clusters and excess neutrons are estimated separately. The calculated values are in a good agreement with the experimental data.

The role of isospin symmetry in collective nuclear structure

The nucleus is a unique laboratory in physics — a quantum many-body system comprising two types of fermion, the neutron and proton, differing in charge but otherwise essentially identical in their behaviour. The fact that the strong interaction between these fermions is largely independent of charge results in striking symmetries in nuclei. This neutron–proton exchange invariance is encompassed in the elegant concept and formalism of Wigner’s isotopic spin — or isospin. The impact of isospin symmetry is maximal near the N=Z line where nuclei have equal numbers of neutrons and protons, and studies involving isospin effects have undergone a resurgence in recent years as such nuclei become more readily accessible. In this review we discuss three isospin-related phenomena: the elegant isospin symmetry of excited analogue states in nuclei, the origin of the extra binding for nuclei with equal numbers of neutrons and protons and the exotic phenomenon of neutron–proton pairing. These three topics, all of considerable current interest, demonstrate the power, simplicity and modern relevance of the isospin concept.

Exact Solution of the Isovector Neutron-Proton Pairing Hamiltonian

The complete exact solution of the T = 1 neutron-proton pairing Hamiltonian is presented in the context of the SO(5) Richardson-Gaudin model with nondegenerate single-particle levels and including isospin symmetry-breaking terms. The power of the method is illustrated with a numerical calculation for for 64Ge for a pf + g9/2 model space which is out of reach of modern shell-model codes.

High spin structure and intruder configurations inP31

The nucleus $^{31}\mathrm{P}$ has been studied in the $^{24}\mathrm{Mg}$($^{16}\mathrm{O}$,2$\ensuremath{\alpha}p$) reaction with a 70-MeV $^{16}\mathrm{O}$ beam. A complex level scheme extended up to spins 17/2${}^{+}$ and 15/2${}^{\ensuremath{-}}$, on positive and negative parity, respectively, has been established. Lifetimes for the new states have been investigated by the Doppler shift attenuation method. Two shell-model calculations have been performed to describe the experimental data, one by using the code ANTOINE in a valence space restricted to the sd shell, and the other by applying the Monte Carlo shell model in a valence space including the $\mathit{sd}\text{\ensuremath{-}}\mathit{fp}$ shells. The latter calculation indicates that intruder excitations, involving the promotion of a $T=0$ proton-neutron pair to the fp shell, play a dominant role in the structure of the positive-parity high-spin states of $^{31}\mathrm{P}$.

Variational Approach to Configuration Interaction

A variational method is developed to determine configuration interaction wave functions. The method is straightforward and is applied to a pairing Hamiltonian with constant matrix elements, for which exact eigenvalues are available. Comparisons are made with the exact results. Calculations can be carried out to any desired degree of accuracy. The method is also applied to a Hamiltonian that has neutron-neutron, proton-proton, and neutron-proton pairing. No difficulties are found in extending the method to this Hamiltonian that has many collective modes. In practice, the method scales linearly with , where is the number of variational basis states.

Minimal models of cooling neutron stars with accreted envelopes

We study the minimal cooling scenario of superfluid neutron stars with nucleon cores, where the direct Urca process is forbidden and the enhanced cooling is produced by the neutrino emission due to Cooper pairing of neutrons. Extending our previous consideration (Gusakov et al. 2004a), we include the effects of accreted envelopes of light elements. We employ phenomenological density-dependent critical temperatures T_{cp}(\rho) and T_{cnt}(\rho) of singlet-state proton and triplet-state neutron pairing in a stellar core, as well as the critical temperature T_{cns}(\rho) of singlet-state neutron pairing in a stellar crust. We show that the presence of accreted envelopes simplifies the interpretation of observations of thermal radiation from isolated neutron stars in the scenario of Gusakov et al. (2004a) and widens the class of models for nucleon superfluidity in neutron star interiors consistent with the observations.

Isospin asymmetry and type-I superconductivity in neutron star matter

It has been argued by Buckley et. al.(Phys. Rev. Lett. 92, 151102, 2004) that nuclear matter is a type-I rather than a type-II superconductor. The suggested mechanism is a strong interaction between neutron and proton Cooper pairs, which arises from an assumed U(2) symmetry of the effective potential, which is supposed to originate in isospin symmetry of the underlying nuclear interactions. To test this claim, we perform an explicit mean-field calculation of the effective potential of the Cooper pairs in a model with a simple four-point pairing interaction. In the neutron star context, matter is very neutron rich with less than 10% protons, so there is no neutron-proton pairing. We find that under these conditions our model shows no interaction between proton Cooper pairs and neutron Cooper pairs at the mean-field level. We estimate the leading contribution beyond mean field and find that it is is small and attractive at weak coupling.

Isospin symmetry breaking in an algebraic pairing Sp(4) model

An exactly solvable $\mathfrak{sp}(4)$ algebraic approach extends beyond the traditional isospin-conserving nuclear interaction to bring forward effects of isospin symmetry breaking and isospin mixing resulting from a two-body nuclear interaction that includes proton-neutron (pn) and like-particle isovector pairing correlations plus significant isoscalar pn interactions. The model yields an estimate for the extent to which isobaric analog ${0}^{+}$ states in light and medium-mass nuclei may mix with one another and reveals possible, but still extremely weak, nonanalog $\ensuremath{\beta}$-decay transitions.

Proton-neutron pairing energies inN=Znuclei at finite temperature

Thermal behavior of isoscalar and isovector proton-neutron (pn) pairing energies at finite temperature are investigated by the shell model calculations. These pn pairing energies can be estimated by double differences of "thermal" energies which are extended from the double differences of binding energies as the indicators of pn pairing energies at zero temperature. We found that the delicate balance between isoscalar and isovector pn pairing energies at zero temperature disappears at finite temperature. When temperature rises, while the isovector pn pairing energy decreases, the isoscalar pn pairing energy rather increases. We discuss also the symmetry energy at finite temperature.

Structure of isomeric states in 66As and 67As

Strong residual correlations between neutrons and protons in N ≈ Z systems can lead to unusual structure. Using the spherical shell model, we show that a low-excitation shape isomer can occur in the odd–odd N = Z nucleus 66As. This extends the picture of shape coexistence beyond even–even nuclei. Furthermore, it is demonstrated that in 66As and in the N = Z + 1 nucleus 67As, a new type of isomer, which we term j-isomer, can be formed. The underlying mechanism for the isomerism formation is structure change in the isomeric states, which involves either an alignment of a neutron–proton pair from the high- j intruder orbitals, or a simultaneous occupation of these neutron and proton high- j orbitals.

NEUTRON–PROTON PAIRING IN 64Ge

Isotopes of germanium are studied in the framework of the relativistic mean-field theory with a δ-pairing type residual interaction. Both pairing channels T=1 and T=0 are included. The T=0 channel does not contribute to the pairing energy even with a large coupling strength of the δ force. It is shown that the Wigner-like term (congruence energy) may be partly reproduced by T=1, Tz=0 neutron-proton pairing which is remarkably strong in the case of Z=N nuclei.

Isospin effects in two-particle correlation functions: A probe for the isospin dependence of the nuclear equation of state

Small-angle two-particle correlation functions, involving neutrons and protons, have been measured for E/A = 61 MeV Ar + Sn-112,Sn-124 collisions, i.e. systems similar in size but with different isospin asymmetry. The correlation strength of neutron-proton (np) and proton-proton (pp) pairs is stronger for the more neutron-rich system, indicating a shorter average emission time for this system. Comparisons with isospin-dependent BUU transport model simulations are presented, and their implications for the density dependence of the nuclear symmetry energy are discussed.

Nucleon-nucleon coincidence measurement in the non-mesonic weak decay of [formula omitted] and [formula omitted] hypernuclei

We have measured both yields of neutron-proton and neutron-neutron pairs emitted from the non-mesonic weak decay process of 5_Lambda-He and 12_Lambda-C hypernuclei produced via the (pi^+,K^+) reaction for the first time. We observed clean back-to-back correlation of the np- and nn-pairs in the coincidence spectra for both hypernuclei. The ratio of those back-to-back pair yields, Nnn / Nnp, must be close to the ratio of neutron- and proton-induced decay widths of the decay, Gn(Lambda n -> nn)/Gp(Lambda p -> np). The obtained ratios for each hypernuclei support recent calculations based on short-range interactions.

High spin structure ofS34and the proton-neutron coupling of intruder states

The nucleus {sup 34}S has been studied up to relatively high spin (I=10({Dirac_h}/2{pi})) and up to an excitation energy of 16.64 MeV. Data are compared with different shell model calculations where effective interactions involving two main shells, the sd and the fp, are used. For the first time in an N{ne}Z nucleus, it is observed that the promotion of an isoscalar (T=0) proton-neutron pair to the fp shell becomes energetically favored at high spin.

Companion problems in quasispin and isospin

We note that the same mathematical results apply to problems involving quasispin and isospin, but the problems per se are different. In the quasispin case, one deals with a system of identical fermions (e.g., neutrons) and addresses the problem of how many seniority-conserving interactions there are. In the isospin case, one deals with a system of both neutrons and protons and the problem in question is the number of neutron-proton pairs with a given total angular momentum. Other companion problems are also discussed.