Theory Of Direct Capture Research Articles

Theory of direct capture from two‐and three‐dimensional reservoirs to quantum dot states

AbstractWe present a comparison of Coulomb scattering rates from a two‐dimensional carrier reservoir/three‐dimensional carrier reservoir and quantum dot states. The scattering rates are microscopically determined in the limit of Born‐Markov approximation.The calculations highlight that, within the considered parameter range the scattering from a two‐dimensional carrier reservoir is more efficient than from a three‐dimensional carrier reservoir. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Thermal-neutron capture byNi58,Ni59, andNi60

We have studied the primary and secondary {gamma} rays (414 in {sup 59}Ni, 390 in {sup 60}Ni, and 240 in {sup 61}Ni) following thermal-neutron capture by the stable {sup 58}Ni, radioactive {sup 59}Ni, and stable {sup 60}Ni isotopes. Most of these {gamma} rays have been incorporated into the corresponding level schemes consisting of 65 levels in {sup 59}Ni, 88 levels in {sup 60}Ni, and 40 levels in {sup 61}Ni. The measured neutron separation energies (S{sub n} in keV) for {sup 59}Ni, {sup 60}Ni, and {sup 61}Ni are, respectively, 8999.28{+-}0.05, 11 387.73{+-}0.05, and 7820.11{+-}0.05. The measured thermal-neutron capture cross sections (in barns) for {sup 58}Ni, {sup 59}Ni, and {sup 60}Ni are, respectively, 4.13{+-}0.05, 73.7{+-}1.8, and 2.34{+-}0.05. In all three cases, primary electric-dipole (E1) transitions account for the bulk of the total capture cross section. We have calculated these E1 partial cross sections (in {sup 59}Ni and {sup 61}Ni) using direct-capture theory and models of compound-nuclear capture. The agreement between theory and experiment is good. The experimental level schemes have been compared with the results from a large-basis shell-model calculation. The agreement was also found to be quite good.

Subramanian Raman

Subramanian Raman, a senior staff member in the physics division at Oak Ridge National Laboratory (ORNL), died 8 April 2003 at his home in Oak Ridge, Tennessee, of complications following heart surgery.Born 2 April 1938 in Kollengode, a small town in southwestern India, Raman, often called “Ram” by his friends and colleagues, received his BE in 1959 from the University of Madras. After failing the eye examination required for employment by the India Railway Co, he decided to apply for a Bank of India study-abroad program. Raman came to the US in 1959 and enrolled in the graduate program at Rensselaer Polytechnic Institute, where he received his MS in electrical engineering in 1961. He did his doctoral work at Pennsylvania State University under the supervision of William Pratt. In 1966, he earned his PhD in physics for his thesis “Energy Levels of 82Kr Populated by 82Br Decay.”In June 1966, Raman joined ORNL to work on the nuclear data project directed by Kay Way. That work provided him insights—into both nuclear structure physics and the power of “horizontal” compilations of properties across a broad range of nuclei—that would guide his research interests throughout his 36-year career at ORNL.Raman established definitive decay schemes for about 35 radionuclides, most of them for the first time, and discovered two new isotopes, potassium-48 and argon-45. In the early 1970s, he made a series of careful measurements to establish reliably the lowest log ft value for a β transition of a particular forbidden type. That work resulted in his landmark paper entitled “Rules for Spin Parity Assignments Based on Log ft Values,” published in Physical Review in 1973. His interest in β decay led to two additional compilations, one on superallowed 0+ → 0+ and isospin-forbidden Fermi transitions and another on mixed Fermi and Gamow–Teller β transitions and isoscalar magnetic moments. He pursued the experimental study of superallowed 0+ → 0+ transitions and studied in detail four of the dozen cases that are presently well established.In the late 1970s, Raman initiated a program of neutron-capture gamma-ray spectroscopy that would significantly influence an entire subfield of nuclear physics. He carried out precise measurements (at both ORNL and Los Alamos) on a large number of nuclei and developed an advanced theory of direct capture for interpreting the observations. His work on the 1+ states in lead-208 was particularly significant. He carried out much of the ORNL work at the Oak Ridge Electron Linear Accelerator, where he was scientific director at the time of his death.During the 1970s, Raman also undertook the measurement of fission cross sections for the higher actinides. That work led to the establishment of the US–UK actinides program (1979–92) and the Japan–US actinides program (1988 to present); he served as a lead US participant in both programs.In his last 15 years, Raman became particularly interested in the system-atics of quadrupole distortions in nuclei. He initially compiled B(E2) values for all even–even nuclei and then published a series of papers in which he developed the systematics and theory of collective behavior in those nuclei.Raman’s outgoing and friendly demeanor was apparent to hundreds of visitors to the ORNL physics division over the years. He organized the weekly technical seminars and served as de facto host for many of them. His ready camera also served to document the division’s social activities.His friends and colleagues will remember Raman for the breadth of his work in nuclear structure physics and his significant contributions to allied fields. We will remember his enthusiastic enjoyment of life in general and science in particular, his interest and concern for friends and colleagues, and his deep love and devotion to his family.Subramanian RamanPPT|High resolution© 2004 American Institute of Physics.

Thermal-neutron capture by 14N

The energies and intensities of 58 \ensuremath{\gamma} rays emitted in thermal-neutron capture by nitrogen (99.63% ${}^{14}\mathrm{N}$) have been measured accurately. A major reason was to establish this reaction as a standard for similar measurements on other nuclides. These \ensuremath{\gamma} rays have been placed between 19 known levels (including the ground state and the capturing state) in ${}^{15}\mathrm{N}.$ The primary \ensuremath{\gamma} rays of both electric dipole $(E1)$ and magnetic dipole $(M1)$ types have been analyzed with existing theories of slow-neutron capture. Unlike many other light nuclides, the cross sections for $E1$ transitions in ${}^{15}\mathrm{N}$ differ drastically from the calculations of pure direct-capture theory. The role of the resonance-capture contribution from the proton-unbound, neutron-bound level at $29\ifmmode\pm\else\textpm\fi{}2\mathrm{keV}$ below the neutron separation energy was considered. Some of the properties of this level are quite well known from the ${}^{14}\mathrm{C}(p,\ensuremath{\gamma})$ reaction, and others can be derived from an R-matrix analysis of the total cross section as a function of neutron energy. The thermal-neutron capture \ensuremath{\gamma}-ray spectrum is different from the proton-capture \ensuremath{\gamma}-ray spectrum, but if proper account is taken of the interference among the compound-nuclear processes, the valence-neutron mechanism, and potential capture, the data can be satisfactorily explained. In the thermal-neutron reaction, compound-nuclear $E1$ and direct-capture $E1$ contributions are of comparable magnitude. Valence-neutron capture forms a significant component of capture by the neutron-bound level at $\ensuremath{-}29\mathrm{keV}.$ Largely destructive interference between compound-nuclear and valence processes in a few transitions in thermal-neutron capture gives rise to a much smaller total cross section than would be obtained from the compound-nuclear process alone. The $M1$ transitions also show some evidence of a direct process but not a dominant one. The magnitudes of the compound-nuclear transitions, both $E1$ and $M1,$ are largely consistent with the values implied by giant resonance theories. The resonance parameters deduced for the $\ensuremath{-}29\ensuremath{-}\mathrm{keV}$ level are: total radiation $\mathrm{w}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}=565\ifmmode\pm\else\textpm\fi{}24\mathrm{}\mathrm{meV},$ $\mathrm{reduced}\mathrm{}\mathrm{neutron}\mathrm{}\mathrm{w}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}=51.6\ifmmode\pm\else\textpm\fi{}0.3\mathrm{}\mathrm{keV}$ (for a channel radius of 3.5 fm), and proton $\mathrm{w}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}=160\ifmmode\pm\else\textpm\fi{}30\mathrm{}\mathrm{meV}.$

Thermal-neutron capture by silicon isotopes.

We have studied primary and secondary \ensuremath{\gamma} rays (46 in $^{29}\mathrm{Si}$, 107 in $^{30}\mathrm{Si}$, and 33 in $^{31}\mathrm{Si}$) following thermal-neutron capture by the stable $^{28}\mathrm{Si}$, $^{29}\mathrm{Si}$, and $^{30}\mathrm{Si}$ isotopes. Almost all of these \ensuremath{\gamma} rays have been incorporated into corresponding level schemes consisting of 12 excited levels in $^{29}\mathrm{Si}$, 28 in $^{30}\mathrm{Si}$, and 9 in $^{31}\mathrm{Si}$. In each case, the observed \ensuremath{\gamma} rays account for nearly 100% of all captures. The measured neutron separation energies for $^{29}\mathrm{Si}$, $^{30}\mathrm{Si}$, and $^{31}\mathrm{Si}$ are 8473.56\ifmmode\pm\else\textpm\fi{}0.04, 10609.24\ifmmode\pm\else\textpm\fi{}0.05, and 6587.40\ifmmode\pm\else\textpm\fi{}0.05 keV, respectively. The measured thermal-neutron capture cross sections for $^{28}\mathrm{Si}$, $^{29}\mathrm{Si}$, and $^{30}\mathrm{Si}$ are 169\ifmmode\pm\else\textpm\fi{}4, 119\ifmmode\pm\else\textpm\fi{}3, and 107\ifmmode\pm\else\textpm\fi{}3 mb, respectively. In all three cases, primary electric-dipole (E1) transitions account for the bulk of the total capture cross section. We have calculated these E1 partial cross sections using direct-capture theory. The agreement between theory and experiment is satisfactory.

Thermal-neutron capture by magnesium isotopes.

We have studied the primary and secondary {gamma} rays (33 in {sup 25}Mg, 212 in {sup 26}Mg, and 35 in {sup 27}Mg) following thermal-neutron capture by the stable {sup 24}Mg, {sup 25}Mg, and {sup 26}Mg isotopes. Almost all of these {gamma} rays have been incorporated into the corresponding level schemes consisting of 9 excited levels in {sup 25}Mg, 55 in {sup 26}Mg, and 10 in {sup 27}Mg. In each case, the observed {gamma} rays account for nearly 100% of all captures. The measured neutron separation energies for {sup 25}Mg, {sup 26}Mg, and {sup 27}Mg are, respectively, 7330.65{plus minus}0.05, 11 093.18{plus minus}0.05, and 6443.40{plus minus}0.05 keV. The measured thermal-neutron capture cross sections for {sup 24}Mg, {sup 25}Mg, and {sup 26}Mg are, respectively, 54.1{plus minus}1.3, 200{plus minus}3, and 39.0{plus minus}0.8 mb. In all three cases, primary electric-dipole ({ital E}1) transitions account for the bulk of the total capture cross section. We have calculated these {ital E}1 partial cross sections using direct-capture theory. We have also speculated on the mechanism responsible for the magnetic-dipole ({ital M}1) transitions which are quite strong in {sup 26}Mg.

Direct thermal neutron capture

The authors discuss the direct capture theory pertaining to primary electric dipole (E1) transitions following slow neutron capture. For light nuclides that they have studied (including 9Be, 12C, 13C, 24Mg, 25Mg, 26Mg, 32S, 33S, 34S, 40Ca, and 44Ca), estimates of direct capture cross sections using optical model potentials with physically realistic parameters are in reasonable agreement with the data. Minor disagreements that exist are consistent with extrapolations to light nuclides of generally accepted formulations of compound nucleus capture. They also discuss the channel capture approximation which is, in general, a good representation of these cross sections in heavier nuclei, particularly if the scattering lengths are not different from the corresponding potential radii. They also draw attention to cases where the use of this formula leads to inaccurate predictions.

Direct E2 neutron capture in light nuclei.

We present an analysis of the E2 strength data recently available from thermal radiative neutron capture within the context of direct capture theory. The radiative capture data require a neutron E2 effective charge identical to the one used in bound state shell model calculations, in marked contrast to the E1 situation. We suggest that this difference has its origin in the nature of the coupling governing the particle-core interaction in E2 and E1 radiative capture processes.

The19F(n, ?)20F reaction

The gamma-ray spectrum emitted following thermal neutron capture in19F has been studied with curved crystal and Ge(Li) spectrometers. From the 109 transitions assigned to20F, 85 have been placed in a level scheme containing 26 levels. An average gammaray multiplicity of 2.8 gammas per neutron capture was observed. The neutron binding energy was found to be 6601.33(14) keV. The experimental level scheme is compared to rotational model predictions. In addition it is shown that the decay of the capture state is non-statistical and that there is a strong correlation between the strengths of excitation of levels by the (n, γ) and (d, p) reactions. Calculations of the partial cross-sections using the direct capture theory of Lane and Lynn give order of magnitude agreement with experiment.

Quantitative test of the Lane-Lynn theory of direct radiative capture of thermal neutrons byC12andC13

The Lane-Lynn theory of direct capture is subjected to a quantitative test in the radiative capture of thermal neutrons by /sup 12/C and /sup 13/C. Strong destructive interference effects are observed for the ground state transitions in /sup 13/C and /sup 14/C as predicted by the theory. An outcome of these investigations is the demonstration of the physical significance of the interaction radius. The theory was applied to deduce a (d,p) spectroscopic factor of 0.060 +- 0.004 for the 6589 keV state of /sup 14/C. In addition, the ratio of the radiative capture cross section of /sup 13/C relative to /sup 12/C was measured as 0.388 +- 0.010.

Evidence for direct mechanism in the128Te(n,γ)129Te reaction at thermal neutron energies

Spectra of γ-rays following thermal neutron capture in128Te have been measured. Partial cross section for the radiative transitions to eight129Te levels with ln=1 have been determined. The experimental data are in a very good quantitative agreement with the theory of direct capture by Lane and Lynn.

Verification of the Lane-Lynn theory of direct neutron capture

Quantitative and detailed comparison between the Lane-Lynn theory of direct capture of thermal neutrons and experimental values shown exceptional agreement for a large body of data in the mass regions around 40 and 140. The 136Xe(n,γ) 137Xe reaction is used to verify the theory. Other examples are also given to illustrate the ability of the theory to predict capture cross sections, coherent-scattering lengths, spins of final states, and (d,p) spectroscopic factors.

On the direct capture to unbound states

Recently a discrepancy between the theory of direct radiative capture to unbound states and experimental results for the reaction 12C(p, γ 1) 13N (2366 keV, unbound) has arisen at low γ-energies (150 keV < E γ < 500 keV). It is shown that this discrepancy can be removed by a careful evaluation of the theoretical expression for the usual theory of direct capture to unbound states.

Interference effects in 12C(p, γ) 13N and direct capture to unbound states

Excitation functions of the capture reaction 12C(p, γ 0) 13N have been obtained at θ γ = 0° and 90° and E p = 150–2500 keV. The results can be explained if a direct radiative capture process, E1(s and d → p), to the ground state in 13N is included in the analysis in addition to the two well-known resonances in this beam energy range [E p = 457( 1 2 +) and 1699 ( 3 2 −) keV] . The direct capture component is enhanced through interference effects with the two resonance amplitudes. From the observed direct capture cross section, a spectroscopic factor of C 2 S( l = 1) = 0.49 ± 0.15 has been deduced for the 1 2 − ground state in 13N. Excitation functions for the reaction 12C(p,γ 1p ∗) 12C have been obtained at θ γ = 0° and 90° and E p = 610–2700 keV. Away from the 1699 keV resonance the capture γ-ray yield is dominated by the direct capture process E1 (p → s) to the 2366 ( 1 2 +) keV unbound state. Above E p = 1 MeV, the observed excitation functions are well reproduced by the direct capture theory to unbound states (bremsstrahlung theory). Below E p = 1 MeV, i.e., E p → 457 keV, the theory diverges in contrast to observation. This discrepancy is well known in bremsstrahlung theory as the “infrared problem”. From the observed direct capture cross sections at E p ⪆ 1 MeV , a spectroscopic factor of C 2 S( l = 0) = 1.02 ± 0.15 has been found for the 2366 ( 1 2 +) keV unbound state. A search for direct capture transitions to the 3512 ( 3 2 −) and 3547 ( 5 2 +) keV unbound states resulted in upper limits of C 2 S( l = 1) ≦ 0.5 and C 2 S( l = 2) ⪅ 1.0, respectively. The results are compared with available stripping data as well as shell-model calculations. The astrophysical aspect of the 12C(p, γ 0) 13N reaction also is discussed.

The direct capture mechanism for intermediate energy nucleons

The validity of the direct capture mechanism for protons and neutrons in the range of 10–40 MeV is discussed. The capture cross sections for several nuclei are investigated in detail and the influence of various optical parameters is discussed. It seems that for the heavier nuclei one can obtain the observed cross sections by direct capture theory. Below 20 MeV one is forced to use optical parameters which are inconsistent with elastic scattering analysis.