th / 9 50 80 18 v 1 1 0 A ug 1 99 5 Direct radiative capture of p - wave neutrons


The neutron direct radiative capture (DRC) process is investigated, highlighting the role of incident p-wave neutrons. A set of calculations is shown for the 12C(n, γ) process at incoming neutron energies up to 500 keV, a crucial region for astrophysics. The cross section for neutron capture leading to loosely bound s, p and d orbits of 13C is well reproduced by the DRC model demonstrating the feasibility of using this reaction channel to study the properties of nuclear wave functions on and outside the nuclear surface. A sensitivity analysis of the results on the neutron-nucleus interaction is performed for incident sas well as p-waves. It turned out that the DRC cross section for p-wave neutrons is insensitive to this interaction, contrary to the case of incident s-wave neutrons. PACS number(s): 25.40Lw,21.10Gv,23.40.Hc Typeset using REVTEX 1 The direct radiative capture (DRC) process of neutrons in the keV energy region has some peculiarity recently revived by theoretical analysis [1] as well as by new experimental results [2–4]. Because of the non-resonant nature of the DRC process, the complications related to the calculation of the compound nucleus wave function in the entrance channel are removed. This is a general feature of all the direct capture processes, including those induced by charged particle reactions. However, because of the lack of the Coulomb interaction, the (n, γ) reaction has salient features which makes it a unique probe for investigating nuclear structure information. In fact, the neutron capture process can be explored in the very low neutron energy region where the reaction mechanism may be fully decoupled from the resonance process. In this way, precise information can be obtained for the structure of the capturing orbit and the relative contribution of the various l-wave components to the cross section can be examined separately. Because the DRC process is essentially taking place on the nuclear surface and in the external region, it has been recently proposed [1] to use this reaction channel to study the properties of nuclear wave functions, in connection with the discovery of the neutron halo of light drip-line nuclei [6]. The same kind of information can also be derived from the inverse reaction channel (Coulomb dissociation) where a strong enhancement of the low-lying dipole mode has been observed [5] and treated as an inverse DRC process [1]. While the DRC of protons and alpha particles have been widely investigated in the energy range from a few hundreds of keV up to several MeV [7], the DRC process of neutrons has been mainly examined at thermal (En = 0.0253 eV) energies where s-wave neutrons are captured into bound p orbits. The DRC formalism for thermal neutrons has been revised by Raman et al. [8]. They have shown in detail how the neutron-nucleus potential strongly affects the capture mechanism of s-wave neutrons in light nuclei, whereas no reference to high energy extension nor to higher partial-wave (including p-waves) contributions was given. On the other hand, we may expect that, as the incoming neutron energy increases the capture of p-wave neutrons into bound s and d orbits comes into play and, under proper conditions, it can be regarded as the dominant capture process. 2 The extension of the capture models required to include p-waves and higher partial waves into the neutron DRC process is the main task of this note. In addition, a sensitivity analysis of the DRC process to the neutron-nucleus potential for energies in the keV region will be performed. We stress that applications of DRC models have been rarely extended to energies higher than thermal. In nuclear astrophysics there have been several applications at neutron energies of interest in the r-process nucleosynthesis [9] and for inhomogeneous big-bang theories [10]. For such kind of applications it is necessary to assess quantitatively the DRC prescriptions in a range of energies from a few up to several hundreds of keV. Here we will briefly revise the DRC model for sand p-wave neutrons and apply it to the calculation of the C(n, γ) cross sections for transitions leading to all the four bound states of C . In particular we will consider realistic wave functions for the initial scattering state and we will focus the attention on the influence of the initial l-wave character on the capture cross section. In the early works on neutron capture reactions [11–14] it was recognized that a capture mechanism, in which the incoming neutron is scattered directly into a final bound state without forming a nuclear compound state, might take place for nuclei where the final state is dominated by a strong single-particle configuration. There have been several formulations of the DRC mechanism differing considerably among each other in the way the incoming channel and the final state are described [13,15,8,1]. In general, because the direct capture process is alternative to the compound nucleus (CN) formation mechanism, we can separate the collision matrix into two components Ui→f = Ui→f (CN) + Ui→f(DRC) (1) where all the quantum numbers necessary to define the initial and final states have been lumped into the notation i and f , respectively. The reaction cross section is given by σi→f = π k2 |Ui→f | (2) where k is the wave number of the relative motion in the entrance channel. Here we will 3 deal only with the DRC part of the collision matrix. The capture cross section for emission of electric dipole radiation (E1) in the transition i → f is given by σn,γ = 16π 9h̄ k γ ē |Q (1 ) i→f | (3) where kγ = ǫγ/h̄c is the emitted γ-ray wave number corresponding to the γ-ray energy ǫγ and ē = −eZ/A is the E1 effective charge for neutrons. The cross section is, therefore, essentially determined by the matrix elements Q (1 ) i→f =< Ψf |T̂|Ψi > (4) where T̂ = rY (θ, φ) is th electric dipole operator. Here, the initial state wave-function Ψi is given by a unit-flux incoming wave in the entrance channel, scattered at the origin by the neutron-nucleus potential. The final state wave-function Ψf is given by the residual nucleus (bound) final state. The radial coordinate r denotes the distance of the incoming neutron with respect to the target nucleus. The entrance channel wave function can be decomposed into spherical (l-wave) components Ψlm(r) ≡ wl(r) Yl,m(θ, φ) rv1/2 (5) where wl(r) depends also on the wave number k and is written, as usual, as wl(r) = i √ π k √ 2l + 1i[Il − UlOl]. (6) Here, the common notation for the asymptotic forms of the incoming and outgoing waves, respectively Il and Ol, has been adopted Il ∼ exp(−ikr + 1 2 ilπ) and Ol ∼ exp(+ikr − 1 2 ilπ). (7) Ul indicates the collision matrix for the scattering process in the entrance channel, v is the incoming neutron velocity and k the corresponding wave number. The matrix elements can be decomposed into the product of three factors Q (1 ) i→f = Iif · Aif · √ S. 4 Radial part: Indicating with ulf (r) the radial part of the final state wave function, the radial overlap integral is given by

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@inproceedings{Mengoni1995th9, title={th / 9 50 80 18 v 1 1 0 A ug 1 99 5 Direct radiative capture of p - wave neutrons}, author={Alberto Mengoni and Takaharu Otsuka and Masayuki Ishihara}, year={1995} }