Bremsstrahlung-weighted Cross Section Research Articles

Three-body force effect in triton dipole sum rules.

We calculated the two- and three-body enhancement factors ${\mathrm{\ensuremath{\kappa}}}_{2}$ and ${\mathrm{\ensuremath{\kappa}}}_{3}$ of the dipole sum rule of the triton, arising respectively from the two- and three-body interactions. We performed consistent calculations taking the same interactions for the triton wave function and for the sum rule. The magnitude of ${\mathrm{\ensuremath{\kappa}}}_{2}$ and ${\mathrm{\ensuremath{\kappa}}}_{3}$ are of the order of 0.80--0.86 and 0.03--0.04, respectively. The calculated integrated cross section and the bremsstrahlung weighted cross section are linearly correlated to the calculated triton binding energy.

Relativistic effects in the sum rules for the d( gamma, p)n reaction.

The integrated and bremsstrahlung-weighted cross section for deuteron photodisintegration have been calculated taking the relativistic one-body charge density and the two-body charge density with its local and nonlocal contributions for several nucleon-nucleon potentials in pseudoscalar and pseudovector pion-nucleon couplings. The relativistic correction lowers the enhancement factor for the soft-core potentials and raises it for the hard-core potentials as well as for the Paris potential which has velocity dependence in it to simulate the effect of the hard core. This increase and decrease pattern of the enhancement factor is found to be related to the maxima of the deuteron ground-state wave functions. Though there are some changes in the enhancement factor for different potentials, they are not large enough to enable us to distinguish between the various hard-core or soft-core nucleon-nucleon potentials.

Relativistic effects in deuteron photoabsorption sum rules

The effect of the relativistic one-body ( Delta rho 1) and two-body ( rho 2) charge density is considered in the Thomas-Reiche-Kuhn deuteron photoabsorption sum rule sigma 0 and in the E1 bremsstrahlung-weighted cross section for different NN potential models. rho 2 includes all the terms, local and non-local, deriving from the one-pion exchange processes, calculated both in pseudoscalar and in pseudovector pi N coupling. Delta rho 1 also includes the kinematical corrections to the wavefunctions. The results are compared with those obtained in the exact calculation of the total cross section for the deuteron photodisintegration process. The remarkable sensitivity of the Delta rho 1 contributions of sigma 0 on the NN potentials is shown to come from the different short-range behaviour of these potentials.

Two-body effects in triton photodisintegration sum rules.

The effect of two-body charge density due to one-pion exchange on the triton photodisintegration sum rules has been investigated. The inclusion of the two-body charge density modifies the Siegert form of the dipole operator, resulting in a change in the enhancement factor and the bremsstrahlung-weighted cross section. The expressions obtained for the integrated and the bremsstrahlung-weighted cross sections are quite general, as all the two- and three-body intermediate states have been included. The numerical work is carried out employing a variational wave function and two-body interactions having only central and tensor components. It is found that the change in the enhancement factor is quite significant (approx.16%) for the pseudoscalar coupling and only about 2% with the pseudovector coupling, and can provide information about the nuclear interaction and theories of meson exchange contributions to the triton photodisintegration sum rules.

Two-body effects in the sum rules for thed(γ, p)nreaction

The integrated and bremsstrahlung-weighted cross sections have been calculated including the one-pion-exchange contributions to the charge density for the Paris, super-soft-core, Yale, Hamada-Johnston, and modified Hamada-Johnston potentials. The contribution of the two-meson exchange to the integrated cross section has been estimated. For velocity independent potentials the change in the enhancement factor due to the meson exchange is found to be approximately the same, but it is a little larger for the velocity dependent (Paris) potential. It is found that contrary to the claim made in the literature the integrated cross section cannot distinguish between the various two-nucleon potentials.NUCLEAR REACTIONS $d(\ensuremath{\gamma}, p)n$, calculated integrated and bremsstrahlung-weighted cross sections; included one- and two-pion exchange contribution.

Bremsstrahlung photo-cross-section for unsymmetric system with resonating-group wave function

Sum rule calculations for the integrated bremsstrahlung-weighted cross-section σb for6Li have been performed with resonating-group wave function in a single channel of alpha and deuteron substructures. The r.m.s. radius of6Li has been also calculated. A reasonable value of σh below pion threshold has been obtained using no adjustable parameters if the lack of space symmetry in the ground-state wave function of6Li is taken into account. The intercluster exchange of particles is shown to be rather important.

Symmetry effect on the sum rule for bremsstrahlung cross-section

The effect of symmetry of the space co-ordinates of the nucleons of a nucleus on the integrated bremsstrahlung-weighted cross-section for electric dipole absorption σb has been investigated. It is found that the relationship of σb to the mean square radius of the nucleus is really model dependent. For a system heavier than Is nuclei, for example,6Li it is shown, in principle, that its σb is directly proportional to the mean square radius of6Li in a simple shell model picture which was believed to be contrary thus far. For a modified shell model wave function σb for6Li has been calculated and found to be close to the experimental value. The correction due to the centre-of-mass motion brings the r.m.s. radius of6Li in exact agreement to the value observed by electron scattering.

Two-body effects in deuteron photoabsorption sum rules

The effect of the two-body charge and current densities is considered in the deuteron photoabsorption sum rules. The modifications induced in the Siegert form of the $E1$ operator give rise to an enhancement factor ${k}_{2}\ensuremath{\simeq}0.2$ over the Thomas-Reiche-Kuhn value of the integrated cross section ${\ensuremath{\sigma}}_{0}$. The bremsstrahlung-weighted cross section ${\ensuremath{\sigma}}_{\ensuremath{-}1}(E1)$ is found practically unchanged with respect to its value in impulse approximation, while ${\ensuremath{\sigma}}_{\ensuremath{-}1}(M1)$ shows a 30% increase. The calculations are performed with hard-core, soft-core, and super-soft-core potentials. The dependence on the potential model is small for ${\ensuremath{\sigma}}_{0}$ and quite negligible for ${\ensuremath{\sigma}}_{\ensuremath{-}1}$.NUCLEAR REACTIONS Two-body charge and current densities, deuteron photoabsorption sum rules.

The effects of two-body correlations in 16O on the bremsstrahlung weighted cross section

The bremsstrahlung weighted cross section σ−1, is calculated for,16O using the linked cluster expansion to introduce two-body correlations. All diagrams up to second order in the G-matrix are calculated. A particular choice is made among these diagrams which are grouped in order to preserve the normalization of the one-body density and of the two-body density. This selection of diagrams is shown to be consistent with an expansion in the number of hole-lines. The correlated value obtained in this way, σ−1 = 14.99 mb, is close to the experimental value σ−1 = 15.10 mb although the calculation might still be subject to improvement.

Photo-disintegration of the deuteron with soft-core potentials

We calculate the photo-disintegration integrated (σint) and bremsstrahlung-weighted (σb) cross sections of the deuteron by applying the sum rules of Levinger and Bethe. In our calculations we use the soft-core potentials of Reid and of Eikemeir and Hackenbroich. Our results for σint and σb agree well with experiments.A common feature of the σint calculations of the deuteron with different realistic potentials is their inability to distinguish between any two realistic potentials. We explain this feature in terms of the range-depth relationship for the potentials. Based on this explanation, we propose a simple model for the calculation of σint of the deuteron which uses the radial S- and D-wave functions for a given potential and the mean values of the central and tensor components of the potential energy operator.

Correlations and dipole excitations in nuclei

A microscopic calculation of the effect of two-body correlations on the distribution of dipole strength in nuclei is presented. Large corrections are found for the bremsstrahlung-weighted cross section. An isospin decomposition of the cross section is made and the effect of correlations on the isoscalar, isovector, and isotensor parts is studied. Large corrections to the isotensor part, initially small in the oscillator model, are confirmed. The effects on the photoabsorption cross section of coupling the ground state to the giant isovector monopole vibration are also investigated. This component describes the relative distortion of corresponding neutron and proton wave functions and is shown to be included in an analog spin function. The dominant effect on ground state expectation values of this distortion is shown to be the result of dynamic distortion rather than isospin impurity.NUCLEAR REACTIONS Effect of dynamical correlations on isospin projected sum rules for dipole absorption.

Photodisintegration cross sections of the deuteron

Employing a variety of local static potentials, the bremsstrahlung-weighted and integrated cross sections for the photodisintegration of the deuteron are calculated. The effect of variation of the tensor force in the two-nucleon Yale potential in a manner as to affect only the D state probability of the deuteron, while leaving the values of the other two-body observables unchanged, is studied. It is found that though the contribution of the central, tensor, and spin–orbit components of the two-nucleon potentials to the integrated cross section may vary significantly, the integrated cross section does not change by more than a few percent. The sensitivity of the integrated cross section to the short-distance features of the two-nucleon local potentials is also studied.

The bremsstrahlung weighted cross section and two-body correlations in nuclei

The effect of two-body correlations on the calculation of the bremsstrahlung weighted cross section σ −1 is investigated for 4He, 16O and 40Ca by making partial sums of the linked cluster expansion. It is found that σ −1 is sensitive to long-range correlations but is quite insensitive to the inclusion of short-range correlations.

The neutron distribution in nuclei from bremsstrahlung-weighted cross-sections

Bremsstrahlung-weighted cross-section (bwcs) measurements may be a decisive step to obtain information about the difference between neutron and proton radii. A model-independent relation is discussed between the total bwcs, the relative intensity of the bwcs of the upper ( T >) fragment of the dipole excitation and the neutron and proton radii.

Sum Rule Photo-Disintegration Cross Sections for the Deuteron with Velocity-Dependent and Hard-Core Potentials

We apply the sum rules of Levinger and Bethe to calculate the integrated cross section[Formula: see text]and the bremsstrahlung-weighted cross section[Formula: see text]for the deuteron in the dipole approximation. In our calculations we use (i) Nestor's velocity-dependent potential and (ii) Reid's hard-core potential. Our results for σint and σb obtained with the velocity-dependent potential of Nestor and the hard-core potential of Reid agree well with experiments.

The photodisintegration of helium

The authors calculate the integrated and the bremsstrahlung-weighted cross sections in the photodisintegration of 4He by applying the sum rules of Levinger and Bethe (1950) and using the velocity- dependent potential of Nestor et al (abstr. A33865 of 1968). The wave function used is a mixture of the 1S0 and the principal 5D0 states, the radial dependence of both these states being Gaussian. They obtain the parameters of the wave function from a variational calculation of the binding energy. The results show good agreement with experiments and with similar calculations using hard-core potentials.

On the relation between hard-core and velocity-dependent potentials

A canonical transformation relating hard-core and velocity-dependent nucleon-nucleon potentials is applied to the Srivastava potential and an equivalent hard-core potential is found. It is shown that the deuteron photonuclear electric-dipole integrated and bremsstrahlung-weighted cross sections resulting from the two equivalent potentials are essentially the same. The reasons for this agreement suggest that differences between the two sets of cross sections may remain small in other nuclei employing this type of potential.

Photodisintegration of the alpha particle with tensor forces and a velocity-dependent potential

We calculate the integrated cross section (σint) and the bremsstrahlung-weighted cross section (σb) for the photodisintegration of the alpha particle by applying the sum rules of Levinger and Bethe. The two-body interaction is assumed to be a mixture of a central part, having a velocity-dependent term, and a tensor part. The ground-state wave function of the alpha particle is taken to be a mixture of the principal 1S0 and 5D0(1) states, whose parameters are obtained from a variational calculation of the binding energy of the alpha particle with the above potential. We find our results for σint and σb to be in reasonable agreement with the experiments.

A new model for trinucleons

The binding energy, the bare form factor and the photodisintegration, bremsstrahlung-weighted and integrated cross sections of the trinucleons (3H and 3He) have been calculated earlier by using a modified Feshbach wave function and a velocity- dependent potential. These properties of trinucleons are recalculated with a modified Irving wave function but using the same velocity-dependent potential giving a better agreement with experiments. This shows that the present model for the trinucleons is much more satisfactory than the earlier model using a modified Feshbach wave function.

Phototriton Cross Section ofLi6

The phototriton cross section of ${\mathrm{Li}}^{6}$ has been measured between 24- and 35-MeV photon energy. This work complements an earlier experiment which established the production of the ${\mathrm{Li}}^{6}(\ensuremath{\gamma},t)$ reaction by giant-resonance photons and measured the cross section between 19 and 24 MeV. The phototriton cross section of ${\mathrm{Li}}^{6}$ falls monotonically from 0.46\ifmmode\pm\else\textpm\fi{}0.24 mb at 19 MeV to 0.11\ifmmode\pm\else\textpm\fi{}0.06 mb at 35 MeV. The integrated ($\ensuremath{\gamma},t$) cross section over this energy interval is 4.9\ifmmode\pm\else\textpm\fi{}2.5 MeV mb. The measured bremsstrahlung-weighted cross section is 0.18\ifmmode\pm\else\textpm\fi{}0.09 mb. Implications concerning the nuclear size are discussed.