Reduced Occupancy of the Deeply Bound0d5/2Neutron State inAr32

Abstract

The 9 Be 32 Ar; 31 ArX reaction, leading to the 5 2 ground state of a nucleus at the proton drip line, has a cross section of 10.4(13) mb at a beam energy of 65:1 MeV=nucleon. This translates into a spectroscopic factor that is only 24(3)% of that predicted by the many-body shell-model theory. We introduce refinements to the eikonal reaction theory used to extract the spectroscopic factor to clarify that this very strong reduction represents an effect of nuclear structure. We suggest that it reflects correlation effects linked to the high neutron separation energy (22.0 MeV) for this state. DOI: 10.1103/PhysRevLett.93.042501 PACS numbers: 24.50.+g, 21.10.Jx, 27.30.+t The nuclear shell model pictures deeply bound nucleons as being in fully occupied states. At and above the surface of the Fermi sea, configuration mixing then leads to occupancies that gradually decrease to zero. This picture is modified in an important way by several correlation effects that are absent from or are described only approximately by effective-interaction theories, such as the shell model. These correlations arise from shortrange, soft-core, and tensor nucleon-nucleon (NN) interactions and from longer-range couplings involving low-lying and giant resonance collective excitations [1]. They result in the physical nucleon occupancies of deeply bound states being reduced and the strength shifted into states up to quite high energies; see Pandharipande et al. [2]. Absolute measurements of nucleon occupancies may therefore quantify these correlation effects. It should be pointed out that nuclear reaction observables probing the spatial behavior of the nucleonic wave functions agree well with the shell model picture. Examples are the characteristic angular distributions of transfer reactions and the longitudinal momentum distributions of the residues in knockout reactions, which identify the orbital angular momentum l of the nucleon states involved.The main body of evidence on nucleon occupancies has come from studies of the e; e 0 p reaction [2,3]. These have shown that in stable nuclei over a broad mass region, the valence proton states have their occupancies quenched by factors of order 0.6 -0.7 relative to the extreme singleparticle values. Recently, evidence has emerged that nucleon knockout reactions with heavy ions, at intermediate energies and in inverse kinematics, offer new possibilities for studying these effects by extending measurements to rare radioactive species and to neutron states. In general, the occupancy is not directly observable, but it is reflected in the spectroscopic factor C 2 S j that measures the overlap of the initial and final states with quantum numbers (l; j) [4]. The reduction factor R s is defined as the ratio of the experimental and theoretical value for the spectroscopic factor, the latter obtained when the valence nucleons are confined to a single major oscillator shell, the sd shell for the cases discussed here. This is consistent with how the reduction factors are defined in the analysis of e; e 0 p ...

Proton and neutron knockout from36Ca

“…Assuming that the radial wave function is reasonable, the small experimental knockout cross section measured for the deeply bound valence neutron (as compared to an eikonal reaction theory) implies a very small spectroscopic factor and supports the strong trend in nucleon correlations with neutron-proton asymmetry that has been observed in similar knockout analyses [4,5]. Such small spectroscopic factors are not predicted by standard SM calculations nor by extrapolations of dispersive optical model fits to nuclear data near stability.…”

“…A reduction factor of less than 1 is indeed expected, as it is well known that SM calculations overestimate the localized spectroscopic strength [3]. However, the latter result (with R s values as small as 0.24 [4]) does not yet have a quantitative explanation.…”

Quasifree (e,e′p) reactions on nuclei with neutron excess

“…Recent experimental information on the spectroscopic factors of drip-line isotopes has been obtained by means of nucleon knockout using intermediate heavy-ion beams [67][68][69]. These results also include neutron data and suggest a strong dependence of the spectroscopic factors on the proton-neutron ratio.…”

Cross sections for one-neutron knock-out from37Ca at intermediate energy

“…The result of the Woods-Saxon parametrization is given in Table I. For the beryllium target nuclei, a Gaussian matter distribution with a radius of 2.36 fm, modulated with Z t /A t for protons and N t /A t for neutrons, was assumed [4,16]. The density distribution of the core was calculated in a Hartree-Fock approach for protons and neutrons separately, first with a SLy4 and then a SkX force.…”

“…In previous knock-out studies of deeply bound valence neutron states, the 1d 5/2 and 2s 1/2 states in 32 Ar and 34 Ar, respectively, significantly smaller R s values have been reported [2,4]. Experimental data from knock-out reactions and electron scattering indicate a systematic correlation between R s and the difference in nucleon separation energy, S, taken as S n − S p and S p − S n for neutron and proton knock-out, respectively [3].…”