Examination of the adiabatic approximation for ( d , p ) reactions

Background: Adiabatic distorted-wave approximation (ADWA) study of three-body (d, p) transfer reactions [G.W. Bailey, N.K. Timofeyuk, and J.A. Tostevin, Phys. Rev. Lett. 117, 162502 (2016)] reported strong sensitivity of cross sections to the neutron-proton (np) interaction model when the nucleon-nucleus optical potential is nonlocal.Purpose: The verification of this unusual finding using more reliable methods is aimed for in the present work.Methods: A rigorous Faddeev-type three-body scattering theory is applied to the study of (d, p) transfer reactions. The equations for transition operators are solved in the momentum-space partial-wave framework.Results: Differential cross sections for 26 Al(d, p) 27 Al reactions are calculated using nonlocal nuclear optical potentials and a number of realistic np potentials. Only a weak dependence on the np force model is observed, typically one order of magnitude lower than in the previous ADWA study. The shape of the angular distribution of the experimental data is well reproduced.Conclusions: Cross sections of (d, p) transfer reactions calculated using a rigorous three-body method show little sensitivity to the np interaction model. This indicates a failure of the ADWA in the context of nonlocal potentials. Some evident shortcomings of the ADWA are pointed out.

Section: Discussionmentioning

confidence: 63%

Weak sensitivity of three-body ( d,p ) reactions to np force models

Deltuva

2018

“…In all cases, the CDCC cross sections are significantly lower than the ADWA ones. Their ratio in the maximum, shown in Table I, in most cases is higher than an average value of 1.25 reported for local optical potentials in [17]. The ratio seems to correlate with the neutron separation energy in the final state: for l = 0 transfer to the final 1/2 + state it decreases with excitation energy.…”

mentioning

confidence: 56%

Reduced sensitivity of the (d,p) cross sections to the deuteron model beyond the adiabatic approximation

Gómez-Ramos

Timofeyuk

2018

It has recently been reported [Phys. Rev. Lett. 117, 162502 (2016)] that (d, p) cross sections can be very sensitive to the n-p interactions used in the adiabatic treatment of deuteron breakup with nonlocal nucleon-target optical potentials. To understand to what extent this sensitivity could originate in the inaccuracy of the adiabatic approximation we have developed a leading-order localequivalent continuum-discretized coupled-channel model that accounts for non-adiabatic effects in the presence of nonlocality of nucleon optical potentials. We have applied our model to the astrophysically relevant reaction 26m Al(d, p) 27 Al using two different n-p potentials associated with the lowest and the highest n-p kinetic energy in the short-range region of their interaction, respectively. Our calculations reveal a significant reduction of the sensitivity to the high n-p momenta thus confirming that it is mostly associated with theoretical uncertainties of the adiabatic approximation itself. The non-adiabatic effects in the presence of nonlocality were found to be stronger than those in the case of the local optical potentials. These results argue for extending the analysis of the (d, p) reactions, measured for spectroscopic studies, beyond the adiabatic approximation.

“…For 40 Ca target the effect of including the 3N force (set III) has an opposite effect to the one seen in the ADWA for both deuteron energies. For 26 Al, this force has a weaker effect on populating the 27 Al ground state than the ADWA does but it shows a slightly stronger influence for the final 27 Al state at E x = 7806 keV. In the latter case the 3N effect is still small, no more than 10% in the maximum.…”

Section: The Watanabe Model With 3n Forcementioning

confidence: 83%

“…This simple exercise demonstrates the important role of the range of the 3N interaction and shows the necessity of using a 3N force model compatible with the NN interaction model. Below, we will proceed with using The adiabatic potential U3N (R) calculated for d+ 26 Al system using hypercentral 3N potential of a fixed volume integral and several values of the hyperradius ρ0.…”

Section: Adiabatic D − a Potential With A Hypercentral 3n Interamentioning

confidence: 99%

“…The ADWA accounts for deuteron breakup only in an approximate way. An exact three-body treatment of deuteron breakup in Faddeev and continuum-discretized coupled channel (CDCC) approaches using local nucleon optical potentials suggests that non-adiabatic corrections can be important (see, for example, [25,26]). Nonadiabatic effects are even stronger when N -A optical potentials, employed in (d, p) calculations, are nonlocal [27].…”

Section: The Watanabe Model With 3n Forcementioning

confidence: 99%

See 1 more Smart Citation

Three-nucleon force contribution in the distorted-wave theory of (d,p) reactions

Timofeyuk

2018

The distorted-wave theory of A(d,p)B reactions, widely used to analyze experimental data, is based on a Hamiltonian that includes only two-nucleon interactions. However, numerous studies of few-nucleon systems and many modern developments in nuclear structure theory show the importance of the three-nucleon (3N ) force. The purpose of this paper is to study the contribution of the 3N force of the simplest possible form to the A(d,p)B reaction amplitude. This contribution is given by a new term that accounts for the interaction of the neutron and proton in the incoming deuteron with one of the target nucleons. This term involves a new type of nuclear matrix elements containing an infinite number of target excitations in addition to the main part associated with the traditional overlap function between A and B. The nuclear matrix elements are calculated for double-closed shell targets within a mean field theory where target excitations are shown to be equivalent to exchanges between valence and core nucleons. These matrix elements can be readily incorporated into available reaction codes if the 3N interaction has a spin-independent zero-range form. Distorted-wave calculations are presented for a contact 3N force with the volume integral fixed by the chiral effective field theory at the next-to-next-to-leading order. For this particular choice, the 3N contribution is noticeable, especially at high deuteron incident energies. No 3N effects are seen for incident energies below the Coulomb barrier. The finite range can significantly affect the 3N contribution to the (d,p) cross sections. Finite-range studies require new formal developments and, therefore, their contribution is preliminarily assessed within the plane-wave Born approximation, together with sensitivity to the choice of the deuteron model. PHYSICAL REVIEW C 97, 054601 (2018) i A n p r r p r n R d R p x i y i B d FIG. 1. Definition of coordinates for an A(d,p)B reaction. where J A M A ( J B M B ) is the wave function of the target (daughter) nucleus with the angular momentum J A (J B ) and its projection M J A (M J B ), ψ J d M d is the incoming deuteron wave function, ψ J p M p is the outgoing proton spin function and J d (J p ) and M J d (M J p ) are the spins and spin projections of the deuteron (proton). Also, χ k d (R d ) is the deuteron distorted wave with momentum k d , obtained either in DWBA or in ADWA, and χ k p (R p ) is the proton distorted wave in the exit channel with momentum k p , while V np is the interaction between n and p in the deuteron. The definitions of all the coordinates are given in Fig. 1. The paper will discuss an additional term which arises in T (d,p) when a 3N force is included. This term has the same structure as Eq. (1) but with V np replaced by i∈A W inp , where W inp is the interaction between n and p from the deuteron and the nucleon i from the target.The present paper calculates the contributions from i∈A W inp using a simple hypercentral model for the 3N force. It starts with discussion in Sec. II of the distorted-wave...