On direct proton decay of the Gamow-Teller giant resonance

The semi-microscopic approach to the description of giant resonances in medium-heavy mass closed-shell nuclei is implemented to treat partial probabilities of direct-proton decay of the Gamow-Teller giant resonance (GTGR) in 208Bi. The corresponding experimental data are reasonably explained.


Introduction
Partial probabilities of direct nucleon decay of giant resonances (GRs) carry information about the particle-hole (ph) structure and damping mechanisms of GRs. Therefore, these probabilities should be related to the main properties of GRs and included in their full description. As applied to medium-heavy mass closed-shell nuclei, this aim can be achieved within the semi-microscopic approach to the description of giant resonances (SMAGR). The present formulation of this approach has been initially given in [1] and then extended to a number of implementations (see the reviews [2,3]). The SMAGR is a generalization of the standard and non-standard versions of the continuum-Random-Phase-Approximation (cRPA) developed to take into account a spreading effect. The latter is described phenomenologically in terms of the energy-dependent imaginary part of an effective optical-model potential directly used in cRPA equations [2,3].
Being the spin-flip partner of the isobaric analog resonance (IAR), the GTGR corresponds to the 1 + collective proton-(neutron-hole)-type nuclear excitations. In spite of a lot of experimental studies of the GTGR (predominantly via the direct (p,n)-and ( 3 He,t)-reactions), the proton decay of the GTGR in 208 Bi has only been studied by the coincident 208 Pb( 3 He,tp) experiments [4]. The same method has later been used for studying proton decay of the GTGR overtone, isovector giant spin-monopole resonance (IVGSMR (−) ) in 208 Bi [5]. The unique experiment on excitation of the GTGR in 118 Sb with the resonance 117 Sn(p,n tot )-reaction [6] should be also mentioned. Along with the anomalously small total width (≃ 1 MeV), the partial (elastic) proton width of the mentioned GTGR has been measured as well.
Using the modern version of the SMAGR [1][2][3], in the present work we revise the previous calculations of the partial direct-proton-decay probabilities performed in [7] for the GTGR in 208 Bi. The new elements of our analysis are: (i) taking the spreading effect on the escapedproton wave function into account; (ii) the use of the energy-averaged decay-channel strength function (instead of the Breit-Wigner parametrization of the proper cRPA strength function); (iii) the use of the proton optical-model penetrability (instead of the penetrability calculated for a a e-mail: safonov@theor.mephi.ru schematic single-particle potential). The method and results briefly described in Sect. 2 will be published soon together with the study of the GT strength distribution in a wide excitation energy interval [8].

Direct-proton-decay probabilities for the GTGR in 208 Bi
As applied to description of charge-exchange excitations, the cRPA radial equations for the basic quantities are given in [7]. Extension of these equations on taking the spreading effect into account is described in [2,3] in a rather schematic form. As applied to the semi-microscopic description of 0 + charge-exchange excitations (including IAR), the radial equations for the energy-averaged basic quantities are explicitly given in [9]. These quantities are: the effective fieldṼ (−) (x, ω) and strength function S (−) (ω), corresponding to an external single-particle field V (−) = V(r)τ (−) (ω is the excitation energy counted off the ground-state energy of the parent (even-even) nucleus); the proton-escape amplitude M (−) ν (ω) and partial protondecay-channel strength function S (−) ν (ω) = |M (−) ν (ω)| 2 (ν = n r , (ν) is the full set of the quantum numbers of a neutronhole state, populated after direct proton decay, (ν) = j ν , l ν ). In the semi-microscopic description of the 1 + chargeexchange excitations we suggest to use, for short, the equations of Ref. [9] after the following substitutions: are the intensities of the isovector part of the Ladau-Migdal particle-hole interaction: F(x 1 , x 2 ) → (F ′ + G ′ σ 1 σ 2 )τ 1 τ 2 δ(r 1 − r 2 ). In Eq.
(2) (π) = j π , l π are the single-proton quantum numbers linked to (ν) via the corresponding selection rules; n ν are the neutron occupation numbers. The partial proton-decaychannel strength functions for the GTGR are properly ,ν (ω). These strength functions determine the corresponding partial direct-protondecay branching ratios as follows:e where integration is performed over the resonance. It is noteworthy that almost the same equations determine within SMAGR the partial branching ratios for direct proton decay of the IVGSMR (−) . The difference is in the choice of the radial dependence of the external field V(r) → R 2 − η, where the scaling parameter η is chosen from the condition of "non-exciting" the GTGR [3,10]. A mean field and particle-hole interaction together with the imaginary part W(r, ω) of the effective opticalmodel potential are the input quantities for calculations within the SMAGR the giant-resonance strength function. The partial direct-nucleon-decay branching ratios are then calculated without the use of additional model parameters. In our calculations a phenomenological mean field and Landau-Migdal interaction are used. The mean-field parameters (together with the parameter f ′ ) are found, as described in [11] but with the use of another meanfield geometrical parameter r 0 = 1.21 fm. In calculations of the strength function of the GTGR in 208 Pb we used two adjustable parameters: the intensity g ′ of the Landau-Migdal interaction to reproduce in calculations the observed GTGR energy; the intensity of W(r, ω) to reproduce in calculations the total width of the considered GTGR. Before comparing the calculated partial direct-protondecay branching ratios b (−) ν of Eq. (3) with the corresponding experimental values, we recalculate the partial protondecay-channel strength functions S (−) (π),ν to take into account two points: (i) the difference of the experimental neutronhole state excitation energies E exp ν of the product nucleus 207 Pb from the calculated energies E ν = ε calc ν − ε calc p 1/2 (ε calc ν are determined by the mean field); (ii) the difference of the experimental spectroscopic factors S ν for the mentioned one-hole states from unity. (Both of these differences are shown in Table 1). In view of the discussed points we recalculate the partial proton-decay-channel strength functions to the following effective values: Here, ε = ε ν + ω is the escaped-proton energy; T (π) (ε) is the optical-model penetrability (the seizure coefficient) for the partial proton wave. Because of changing over the GTGR the potential-barrier penetrability for escaped protons, the energy dependence of the calculated decaychannel strength functionsŠ (−) ν (ω) is noticeably different from that of the giant-resonance strength function S (−) (ω) (figure 1). The proton branching ratiosb ν calculated for the GTGR in 208 Bi in accordance with Eqs. (3), (4) for the energy interval ω = 12-26 MeV are found in a reasonable agreement with the corresponding experimental data (Table 1).
In conclusion of this Section we note, that the similar description of the partial (and total) direct-proton-decay  Table 1. The calculated partial direct-proton-decay branching ratios for the GTGR in 208 Bi in a comparison with the experimental data. Some characteristics of the decay channels are also given. branching ratios for the IVGSMR (−) in 208 Bi leads to different results [3,10]. The total branching ratios (about 50%) is in reasonable agreement with the experimental data of [5], while the calculated and experimental distributions of the partial branching ratios over decay channels are noticeably different: population of deep neutron-hole states in 207 Pb has been unexpectedly observed in [5]. Up to now there is no explanation of this observation.