A unique aspect of proton-rich
nuclei with is that neutrons and protons occupy the same
single-particle orbitals. Consequently,
due to the large spatial overlaps between neutron
and proton single-particle wave functions, pn pairing is expected to be
present in those systems.
So far, the strongest evidence for enhanced pn correlations
around the =
line comes from the
measured binding energies [8,9,10,11,12,13,14,15,16]
and the isospin structure of
the low-lying states in odd-odd nuclei
[17,18,19,20,21,22,23,24,,26,27,28,16].
The pn correlations are
also expected to
play some role in single-beta decay [29,30,31], double-beta decay
[32,33,34,35,36,37,38],
transfer reactions [39,40,41,42,43,44,45]
(see, however, Ref. [16]),
structure of low-lying collective states
[46], alpha decay and alpha correlations
[47,48,49,50,45,51,52],
structure of high spin states
[20,53,54,55,56,57,58,59,60,,62,63,64,65,66,67,,69,70,71,72,14,73,74,75,,77,78,79],
and in properties of low-density nuclear matter
[80,81,82,83,84,85,86,87,88,89,90].
Actually, the pn pairing is not ``the new kid on the block" but it has a long history and is ultimately connected to the charge invariance of the strong Hamiltonian. (For reference, in 1932 Heisenberg introduced isotopic spin [91] and in 1936 Wigner introduced the nuclear SU(4) supermultiplets [92].) An important step was the adaptation of Racah's concept of seniority by Racah and Talmi [93], and Flowers [94] in 1952. In the independent quasiparticle (BCS) picture [95], pairing condensate appears as a result of an attractive interaction between quasiparticles near the Fermi surface. The term ``nuclear superconductivity" was first used by Pines at the 1957 Rehovot Conference to point out that the new BCS theory might also apply to nuclei [96]. This was formally accomplished in the late fifties [97,98] and shortly afterwards the importance of pn pairing was emphasized [99,47,100] and a number of theoretical papers dealing with the generalization of the BCS theory to the pn pairing case appeared [101,102,103].
Independently, group-theoretical methods
based on the
quasi-spin formalism were developed. Many insights were gained
by simple solvable models employing symmetry-dictated interactions
[104,105,106,107,108,109,110,111].
Two families of models were used, one based on the
-
coupling with the symmetry SO(5) (appropriate for the
=1 pairing) and the other based on the
-
coupling
with the symmetry SO(8) (appropriate for the
=0 and
=1 pairing). These models have been consecutively
developed and applied to various physically interesting
cases [42,44,112,36,45,113,114].
Among many techniques used to solve the problem of pn pairing with
schematic interactions,
worth mentioning are the exact methods [115,116,43]
used to describe isovector states of a charge-independent
pairing Hamiltonian.
Properties of pn pairing (at low and high spins,
in cold and hot nuclei) have been studied within
the large-scale shell model
(diagonalization shell-model, variational shell model,
and Monte Carlo shell model)
[90,117,118,69,70,119,120,121,,64,123,20,21].
It was concluded that the
isovector pairing in the dominating =0 channel
mainly acts between time-reversed states
within the same shell. On the other hand, isoscalar pairing can
also involve coupling (mainly
=1)
between spin-orbit partners. Consequently, spin-orbit
splitting plays a crucial role in understanding the
=0 pairing [20].
It is to be noted that it is by no means obvious how to extract
``pairing correlations" from the realistic shell-model calculations.
The ``pairing Hamiltonian" is an integral part of the
residual shell-model interaction.
The shell-model Hamiltonian is usually written in the
p-p representation, but it also can be transformed
to the p-h representation by means of the Pandya
transformation [124]. This means that the
high- interaction between pairs can translate into
the low-
interaction in the p-h channel. It is only in the mean-field theory that the division
into ``particle-hole" and ``particle-particle" channels
appears naturally. One way of translating the shell-model results into
mean-field language is by means of correlators, such
as the number of
=0 and
=1 pairs in the shell-model wave function,
[112,120,125,69].
The extension of the Interacting Boson Models (IBM)
to the case of pn bosons had to wait until 1980, when
IBM-3 (only =1 pairs
[126]) and IBM-4 [both (
=1,
=0) and (
=0,
=1) bosons
[127]] were proposed.
For recent applications of various algebraic models, see
Refs. [128,129,,131,132,133,134,135,136,137,26,138].
An alternative strategy to the pn pairing problem is via the mean-field approach. Here, the major conceptional step was the proposition that quasiparticles are mixtures not only particles and holes but also protons and neutrons. The resulting HFB quasi-particle vacuum is a superposition of wave functions corresponding to even-even and odd-odd nuclei with different particle numbers. Unlike in the standard nn and pp pairing cases, the coefficients of the Bogoliubov transformation are, in general, complex. Generalized Bogoliubov transformation, generalized gap equations, and pn pairing fields are discussed in Refs. [101,139,140,141,142,143,144,,146,147,148,,150,151,152,,53,154,155,156,55,,57,157,62,65,158,67,68,159,160,161].
The problem of the
spontaneous isospin breaking in the mean-field theory
was realized soon after the development
of the generalized quasiparticle approach [144,148,48].
The symmetry is broken by the
independent (separate) treatment of =1
proton and neutron pairing correlations and by the
BCS quasiparticle mean field (the generalized product wave
function is not an eigenstate of isospin). Several techniques have been developed
to restore isospin. They include the Generator Coordinate Method, RPA,
Kamlah expansion, iso-cranking, and exact projection
[144,148,48,162,163,37,164,67,,165,166,15,16].
It is fair to say, however, that in spite of
many attempts to extend the
quasiparticle approach to incorporate the effect
of pn correlations, no symmetry-unrestricted mean-field calculations of pn
pairing, based on realistic effective interaction and
the isospin-conserving formalism
have been carried out.