Coulomb Displacement Energies Research Articles

Nucleon-nucleon correlations and the Coulomb Displacement Energy

Coulomb Displacement Energies (CDE) are accurately known for a wide range of nuclear masses. Assuming isospin independence in the nuclear Hamiltonian, the CDE can in first instance be interpreted as the Coulomb interaction energy between the density of the excess neutrons and the proton charge density in the parent nucleus. However, when using reasonable meanfield models for the proton and neutron density one underestimates the CDE by about 8% on average. This discrepancy is known as the Nolen-Shiffer anomaly, and various explanations have been put forward in the past. In this work we reexamine the role of nucleon-nucleon correlations. We present calculations for the pair density functions in various nuclei. Preliminary results suggest that the modifications to the mean-field pair density functions cause an enhancement of the CDE in the order of 4%, which is ratherA-independent.

Nuclear sizes and the Coulomb Displacement Energy

Data on Coulomb Displacement Energies in the mass rangeA=40−240 are analyzed in the deformed Liquid Drop model and in the independent particle model. Reduced half-widths of Woods-Saxon mean-field potential of the resulting neutron-excess distributions are deduced. It is argued that the Nolen-Schiffer anomaly may be lifted by allowing for a slight binding-energy dependence of the mean-field potential geometry.

Isobaric analog state of 11Li

The isobaric analog state (IAS) of the halo nucleus 11 Li has been investigated using the charge exchange reaction 11 Li(p,n) 11 Be ∗ in inverse kinematics at E( 11 Li ) = 64A MeV . The IAS was observed in 11 Be, for the first time, at an excitation energy of 21.16 ± 0.02 MeV with a width of 0.49 ± 0.07 MeV (FWHM). The unit cross section, distortion factor and effective N - N interaction associated with the Fermi transition are extracted. Coulomb displacement energy, decay width, reaction variables and their relation to the halo structure are discussed.

COULOMB DISPLACEMENT ENERGIES BETWEEN ANALOG LEVELS FOR 3 ≤A≤ 239

Experimental Coulomb displacement energies between some 2300 pairs of isobaric analog levels for nuclei 3 ≤A≤ 239 are tabulated. The literature through October 1, 1996, was consulted. Compared to our earlier tables [Atomic Data and Nuclear Data Tables33,447 (1985):A= 3–45;40,9 (1988):A= 44–239], this compilation has expanded by about 40%, and uncertainties have been reduced for many of the previously listed values.

Analysis of Coulomb displacement energies and its relation to the proton halo structure of nuclei

We investigate the Coulomb displacement energies of the nuclear systems16O core plus several nucleons. This analysis is performed in order to search for peculiarities of the nucleus20Mg which was experimentally found to be a candidate for the occurrence of a proton halo. The structure of20Mg is discussed on the basis of this analysis. Some evidence is presented that proton correlations play an important role in the structure of this nucleus.

Stability of proton-rich nuclei in the upper sd shell and lower pf shell.

The decay properties of proton-rich nuclei with Z=19--30 are investigated using measured binding energies of the analog neutron-rich nuclei and Coulomb energy shifts deduced from a parametrization of measured Coulomb displacement energies. Predicted binding energies and separation energies are compared where possible with previous calculations; in most cases the calculations agree within the quoted uncertainties. The positions of the one-proton and diproton drip lines are determined from the calculated separation energies. It is suggested that good candidates for the observation of correlated two-proton emission are $^{34}\mathrm{Ca}$, $^{38,39}\mathrm{Ti}$, $^{45}\mathrm{Fe}$, $^{48}\mathrm{Ni}$, and $^{54}\mathrm{Zn}$. \textcopyright{} 1996 The American Physical Society.

Coulomb displacement energy and the low-energy astrophysical S17 factor for the 7Be(p,γ)8B reaction

Abstract The relationship between the Coulomb displacement energy for the A = 8, J = 2 + , T = 1 state and the low-energy astrophysical S 17 factor for the 7 Be(p,γ) 8 B reaction is discussed. The displacement energy is interpreted in a particle-hole model. The dependence of the particle displacement energy on the potential well geometry is investigated and is used to relate the particle displacement energy to the rms radius and the asymptotic normalization of the valence proton wave function in 8 B. The asymptotic normalization is used to calculate the astrophysical S 17 factor for the 7 Be(p,γ) reaction. The relationship to the 7 Li(n,γ) reaction, the 8 B quadrupole moment, radial density, and break-up momentum distribution are also discussed.

New stellar reaction rates for 25Mg(p, gamma )26Al and 25Al(p, gamma )26Si.

Existing experimental proton stripping reaction data on {sup 25}Mg leading to threshold states in {sup 26}Al are reinvestigated and reanalyzed in a consistent and improved manner. We use unbound state form factors in the DWBA analysis of the measured deuteron angular distributions to deduce absolute rather than relative proton partial widths. For higher-lying resonances these values are compared to widths obtained from ({ital p},{gamma}) work. It is also shown that several of the unique {ital J}{sup {pi}} values assigned previously to {sup 26}Al states are erroneous. This paper reports on a reanalysis of spins, parities, and isospins for {sup 26}Al states located at {ital E}{sub {ital x}}{lt}8.00 MeV. We deduce new stellar rates for the reaction {sup 25}Mg({ital p},{gamma}){sup 26}Al and compare our results with previous values. Furthermore, shell-model calculations for the mass {ital A}=26 system are performed. Theoretical excitation energies, {ital J}{sup {pi}} values, {gamma}-ray transition strengths, spectroscopic factors, and proton partial widths are compared to experimental data and new shell-model assignments of experimental states in {sup 26}Al are derived. We estimate Coulomb displacement energies of excited {sup 26}Mg and {sup 26}Si mirror states and present new analog assignments for {ital T}=1 triplet states in {ital A}=26 nuclei. Basedmore » on shell-model results and analog state information we present updated stellar rates for the {sup 25}Al({ital p},{gamma}){sup 26}Si reaction. {copyright} {ital 1996 The American Physical Society.}« less

Recoil-separated gamma-ray spectroscopy of 47Ti, 47V, 47Cr, 48V, and 48Cr.

High-spin states in the nuclei {sup 47}Ti, {sup 47}V, {sup 47}Cr, {sup 48}V, and {sup 48}Cr have been observed using the reaction {sup 40}Ca+{sup 10}B at {ital E}({sup 40}Ca)=150 MeV. The prompt {gamma} rays were detected in an array of nineteen escape-suppressed Ge detectors in coincidence with the recoiling nuclei which were identified in {ital A} and {ital Z} with a recoil separator. Rotational structures were observed in all these nuclei, apart from {sup 47}Ti, up to spins near the maximum for the ({ital f}{sub 7/2}){sup {ital z}+{ital n}} configuration. A rapid increase in the Coulomb displacement energy for mirror states in {sup 47}V and {sup 47}Cr occurs at {ital J}{sup {pi}}=25/2{sup {minus}}. A backbend occurs in {sup 48}Cr at {ital J}{sup {pi}}=10{sup +}.

Multichannel study on the fragmentation of the 1g9/2isobaric analog resonance inMn53

Fragments of the 1[ital g][sub 9/2] isobaric analog resonance in [sup 53]Mn corresponding to the 3.715 MeV state ([ital S][sub [ital n]]=0.57) in [sup 53]Cr were located using the [sup 52]Cr([ital p],[ital p][sub 0]), [sup 52]Cr([ital p],[ital p][sub 1]), [sup 52]Cr([ital p],[ital p][sub 1][gamma]), [sup 52]Cr([ital p],[ital p][sub 2][gamma]), and [sup 52]Cr([ital p],[gamma])[sup 53]Mn reactions. Differential cross sections were measured in the 4.06--4.28 MeV, and the [gamma]-excitation curves in the 4.04--4.35 MeV proton energy region. Spins, parities, and partial widths were determined with the aid of [ital R]-matrix analysis for all resonances observed in the region. The spins of the 1[ital g][sub 9/2] resonance fragments were found independently from ([ital p],[ital p][sub 1][gamma]), ([ital p],[ital p][sub 2][gamma]), and ([ital p],[gamma]) angular distribution measurements and their analyses. Nineteen fragments were identified and their [gamma]-branching ratios to low lying levels of [sup 53]Mn were also deduced. Partial widths for each fragment in all four channels were derived. Channel-channel correlations were calculated. Fine structure analyses were carried out in all open channels. Inelastic spectroscopic factors and Coulomb displacement energy for the 1[ital g][sub 9/2] state were also derived.

Beta-delayed proton decay of 73Sr.

The ${\mathit{T}}_{\mathit{z}}$=-3/2, A=4n+1 nuclide $^{73}\mathrm{Sr}$ produced in the $^{40}\mathrm{Ca}$${(}^{36}$Ar,3n) reaction has been observed via beta-delayed proton emission. A single proton group at a laboratory energy of 3.75\ifmmode\pm\else\textpm\fi{}0.04 MeV has been observed, corresponding to decay of the T=3/2 isobaric analog state in $^{73}\mathrm{Rb}$ to the ground state of $^{72}\mathrm{Kr}$. Combining this measurement with a Coulomb displacement energy calculation yields a mass excess for $^{73}\mathrm{Sr}$ of -31.82\ifmmode\pm\else\textpm\fi{}0.24 MeV based on a predicted mass for $^{72}\mathrm{Kr}$ of -53.94\ifmmode\pm\else\textpm\fi{}0.24 MeV.

Beta-delayed proton decay of 65Se.

The ${\mathit{T}}_{\mathit{Z}}$=-3/2, A=4n+1 nuclide $^{65}\mathrm{Se}$ produced in the $^{40}\mathrm{Ca}$${(}^{28}$Si,3n) reaction has been observed via beta-delayed proton emission. A single proton group at 3.55\ifmmode\pm\else\textpm\fi{}0.03 MeV has been observed, corresponding to the decay of the T=3/3 isobaric analog state in $^{65}\mathrm{As}$ to the ground state of $^{64}\mathrm{Ge}$. Combining this measurement with a Coulomb displacement energy calculation yields a mass excess for $^{65}\mathrm{Se}$ of -33.41\ifmmode\pm\else\textpm\fi{}0.26 MeV.

Charge independence and charge symmetry breaking interactions and the Coulomb energy anomaly in isobaric analog states.

Effects of CIB (charge independence breaking) and CSB (charge symmetry breaking) interactions on the Coulomb displacement energies of isobaric analog states are investigated for $^{48}\mathrm{Ca}$, $^{90}\mathrm{Zr}$, and $^{208}\mathrm{Pb}$. The mass number dependence of the Coulomb energy anomalies is well explained when we employ CIB and CSB interactions which reproduce the differences of the scattering lengths as well as those of the effective ranges of low energy nucleon-nucleon scattering.

Coulomb displacement energies in relativistic and non-relativistic self-consistent models

Coulomb displacement energies in mirror nuclei are comparatively analyzed in Dirac-Hartree and Skyrme-Hartree-Fock models. Using a non-linear effective lagrangian fitted on ground-state properties of finite nuclei, it is found that the predictions of relativistic models are lower than those of Hartree-Fock calculations with a Skyrme force. The main sources of reduction are the kinetic energy and the Coulomb-nuclear interference potential. The discrepancy with the data is larger than in the Skyrme-Hartree-Fock case.

Beta-delayed two-proton decay of39Ti

The beta-delayed two-proton decay of theT z =−5/2 nuclide39Ti has been observed. The39Sc isobaric analog state has been calculated to lie at 8.82 MeV using the measured two-proton sum energy of 4750±40 keV for its decay to the37K ground state. Combining this excitation energy with a Coulomb displacement energy calculation has lowered the energy available for ground state two-proton emission of39Ti from 760 to 530 keV.

Comment on QCD effects in the nuclear medium, the effective nucleon mass and the Nolen-Schiffer anomaly

We comment on the recently discussed corrections to Coulomb displacement energies in nuclei resulting from the medium dependence of hadronic properties in nuclei. We argue that a particular contribution suggested recently and related to the density dependence of the proton and neutron effective masses should not be added to the previously calculated Coulomb displacement energies.

Non-spin-flip ( 3He, t) charge-exchange and isobaric analog states of actinide nuclei studied at [formula omitted] and 200 MeV

The ( 3He, t) charge-exchange reaction has been studied at θ = 0° and bombarding energies of E( 3 He) = 76.5 MeV and 200 MeV . Spectra were measured using magnetic analysis for target nuclei of 12, 13C, 16O, 19F, 28, 29, 30Si, 90Zr, 117, 120Sn, natTa, natW, 197Au, 208Pb, 230, 232Th, 234, 236, 238U and 244Pu. The measurements at 76.5 MeV concentrated on the isobaric analog states of several actinide nuclei, particularly on their widths and the branching ratios for proton decay. Cross sections, Q-values and total widths were determined for the transitions to the isobaric analog states. Coulomb displacement energies derived from the measured Q-values display the influence of deformed nuclear shapes. Escape widths Γ ↑ and spreading widths Γ ↓ of the isobaric analog states in five actinide nuclei were deduced from the measured proton-decay branching ratios. They were found to be in agreement with predictions which postulate isospin mixing via the Coulomb force with the ( T 0−1)-component of the isovector giant monopole resonance. The measurements at 200 MeV were concerned with transitions to isobaric analog states in both light and heavy nuclei, including several actinide nuclei, but Gamow-Teller resonances and transitions to numerous other states were also observed. The measured cross sections for several transitions to isobaric analog states from 30Si to 208Pb were used to extract the effective interaction V τ for non-spin-flip ( 3He, t) charge exchange at E( 3 He) ≈ 200 MeV . The interaction strength V τ decreases by a factor 0.6 when compared to previously measured values for the energy range E( 3 He) = 65 to 90 MeV . An angular distribution from θ τ = 0° to 16° for the transition to the isobaric analog state in 120Sb measured at E( 3 He) = 200 MeV was found to be in very good agreement with microscopic calculations.

Coulomb displacement energies and bandcrossing phenomena

Abstract The angular momentum dependence of Coulomb energies is explored in the context of a cranked shell model approach. It is observed that a bandcrossing corresponding to the alignment of protons results in a substantial decrease in the Coulomb energy. Recently measured Coulomb displacement energies in 49 Cr and 49 Mn are shown to be consistent with this rotational alignment interpretation.

Coulomb energies and the shell model

Phenomenological shell-model Coulomb energy equations with coefficients varying as A − 1 3 are considered. The highly regular systematics of Coulomb displacement energies is presented and discussed. In a global fit with 22 adjustable parameters the equations reproduce 377 displacement energies with a standard deviation of 55 keV. The relations to other shell-model equations are discussed. The numerical values of the adjusted coefficients are related to the charge radius and deformation parameters of the liquid drop model. The calculation of total Coulomb energies for ground states is considered.

Spectroscopy of 32Cl nucleus via the 32S( 3He, t) 32 Cl reaction at 34.5 MeV

The 32S( 3He, t) 32Cl reaction was studied at 34.5 MeV incident energy. Thirty-four energy levels were identified in 32Cl. Spectroscopic information was derived from the angular distribution shapes for twenty-six levels and corroborated by Coulomb displacement energy calculations. Our level scheme for 32Cl corresponds very well to that for 32P up to E x ∼ 3 MeV.