Isospin-forbidden electric dipole capture and the α(d, γ)⁶Li reaction

Abstract

At the long-wavelength approximation, E1 transitions are forbidden between isospin-zero states.Hence E1 radiative capture is strongly hindered in reactions involving N = Z nuclei but the E1 astrophysical S factor may remain comparable to, or larger than, the E2 one. Theoretical expressions of the isoscalar and isovector contributions to E1 capture are analyzed in microscopic and three-body approaches in the context of the α(d, γ) 6 Li reaction. The lowest non-vanishing terms of the operators are derived and the dominant contributions to matrix elements are discussed.The astrophysical S factor computed with some of these contributions in a three-body α + n + p model is in agreement with the recent low-energy experimental data of the LUNA collaboration.This confirms that a correct treatment of the isovector E1 transitions involving small isospin-one admixtures in the wave functions should be able to provide an explanation of the data without adjustable parameter. The exact-masses prescription which is often used to avoid the disappearance of the E1 matrix element in potential models is not founded at the microscopic level and should not be used for such reactions. The importance of capture components from an initial S scattering wave is also discussed. PACS numbers: 25.40.Lw,23.20.-g,21.10.Hw,21.60.Gx * dbaye@ulb.ac.be † tursune@inp.uz In some radiative-capture reactions between light nuclei, electric-dipole transitions are strongly suppressed [1]. This effect is due to an isospin selection rule: E1 transitions are isospin-forbidden in capture reactions involving N = Z nuclei [2].At the long-wavelength approximation, which is a good approximation for this type of reactions, the isoscalar part of the E1 operator vanishes and transitions take place via its isovector part. Matrix elements of isovector operators vanish between isospin-zero states. However, except for the deuteron, realistic wave functions of N = Z nuclei are not pure eigenstates of the isospin operator and E1 transitions are not exactly forbidden. Their strength may keep an order of magnitude similar to the strength of the usually much weaker E2 transitions. This effect is particularly spectacular for the 12 C(α, γ) 16 O reaction where the isospin-forbidden E1 component is enhanced by resonances (see references in Ref. [1]). Disentangling the E1 and E2 strengths is experimentally very difficult and the theoretical calculations of the E1 component are still quite uncertain. The role of E1 transitions is also complicated in other reactions of astrophysical interest such as d(d, γ) 4 He, 4 He(d, γ) 6 Li, and 16 O(α, γ) 20 Ne. It may also play some role in the triple α mechanism generating 12 C. An ab initio description of the two lightest cases is in principle possible at present. The astrophysical S factor of the d(d, γ) 4 He reaction has been computed with an ab initio calculation in Ref. [3]. The E1 component is mainly obtained from T = 1 isospin components in 4 He introduced by coupled p+ 3 H and n+ 3 He configurations. Its largest contribution reache...

Influence of orthogonalization procedure on astrophysical S-factor for the direct α + d →6Li + γ capture process in a three-body model

“…wave function used in the OPP method has a norm square of about 5.27×10 −3 , while in the case of the SUSY method it is 1.10×10 −4 . As we noted above, the important isotriplet component of the final 6 Li ground state is responsible for the E1 astrophysical S-factor in the α(d, γ) 6 Li direct capture reaction. Therefore, the above difference should yield the same effect for the E1 S-factor.…”

“…As was shown in Ref. [6] in detail, the so-called exact mass prescription, used in the literature for the estimation of the E1 astrophysical S-factor during a long period [8][9][10][11][12], has no microscopic background at all. Some models even neglect this important contribution to the S-factor [13,14].…”

“…Some models even neglect this important contribution to the S-factor [13,14]. As was shown within the frame of three-body model based on the hyperspherical Lagrange mesh method [6,7], the E1 S-factor is dominant in the low energy region E < 100 keV, while the E2 S-factor is mostly important at higher energies. As a result, the new data of the LUNA collaboration for the astrophysical S-factor at low energies have been reproduced with a good accuracy.…”

“…On the other hand, the final three-body α + p + n hyperspherical wave function of 6 Li was calculated with the Voronchev et al αN -potentials [15] with a forbidden state in the S-wave. The forbidden states in the three-body system have been treated within the method 2 of orthogonalising pseudopotentials (OPP) [16].…”

“…The wave function has a small isotriplet component of about 0.5 percent. This important isotriplet part of the three-body wave function [5][6][7] enables one to estimate the forbidden E1 S-factor in a consistent way without using any exact mass prescription. An important question is, how sensitive are the results for the estimated astrophysical S-factor on the projecting method used in the variational calculations of the three-body wave function.…”