Sum Rule Strength Research Articles

Magnetic electron scattering —comparison with other reactions

The recent progress in the study of high-spin magnetic observables in medium and heavy nuclei is reviewed. The electron scattering measurements of elastic high multipolarity magnetic scattering have mapped various aspects of nuclear spin-magnetism in the ground state. When using the precise radial information and the occupancy α of the unpaired nucleon wave function in a reanalysis of single nucleon transfer reactions, a large fraction of the sumrule strength of spectroscopic factors appears to be missing. This may have an impact on the usual assumptions about the strength of ground-state correlations in nuclei. However, the effect of meson exchange currents on the spin operator must be evaluated in detail before a clear picture may emerge.

Gamow-Teller Resonances

Data from recent (p, n) and (3He, t) experiments at intermediate energies are presented. The reactions show a spectacular selectivity for excitation of isospin-spin modes in nuclei. From the zero degree (p, n) spectra Gamov-Teller strength can be deduced, and only half the sumrule strength is observed. The very general nature of the sumrule for charge exchange modes suggests that internal degrees of freedom of the nucleon could be involved. The (3He, t) reaction at 2 GeV shows a strong excitation of the Δ-resonance, indicating that this resonance could be important for the isospin-spin excitations in nuclei.

Compression mode strength inPb208

Compression modes are characterized as volume oscillations of the nucleus which do not contribute to the photonuclear sum rule but show up as concentrated strength in, e.g., inelastic hadronic scattering. Comparison of the nuclear response to different operators in the frame of a continuum random phase approximation is the theoretical technique used to search for such compression modes. Sharply concentrated strength is found only for the breathing mode and the isoscalar dipole mode. Large widths are expected for the isovector monopole, the isovector dipole compression mode, and the isoscalar quadrupole compression mode. For those modes whose escape width corresponds to a large fraction of the total width, one suggests the possibility of detecting them in coincidence experiments by observation of the decaying particle.NUCLEAR STRUCTURE $^{208}\mathrm{Pb}$; calculated compression mode sum rule strength. Random phase method, Landau-Migdal interaction.

Excitation of giant resonances inZr92by inelastic scattering of 115 MeV protons

The differential cross sections for the excitation of giant resonances in $^{92}\mathrm{Zr}$ have been measured in the angular range 14 to 30\ifmmode^\circ\else\textdegree\fi{} by inelastic scattering of 115 MeV protons. The low energy octupole region ${E}_{x}=5\ensuremath{-}10.5$ MeV can be explained as due to excitation of $L=3$ and $L=4$ multipoles. The composition of the differential cross section for the giant resonance region (${E}_{x}\ensuremath{\simeq}10.5\ensuremath{-}20$ MeV) can be described in terms of the percentage energy-weighted sum-rule strength as \ensuremath{\simeq} 63% giant monopole resonance, \ensuremath{\simeq} 65% giant dipole resonance, \ensuremath{\simeq} 48% giant quadrupole resonance, and \ensuremath{\simeq} 20% $L=4$ resonance.

New evidence for deep-lying hole strength in 115Sn and 207Pb via the ( 3He, α) reaction at 283 MeV

It is found that neutron pick-up cross sections up to 50 MeV excitation energy in 115Sn and 207Pb may account for the total sum rule strength of all inner shells. The 115Sn spectrum exhibits much more pronounced structure than that for 207Pb; in particular the results give first evidence for a concentration of the 1 f 7 2 strength in a bump centered aroudn 15 MeV. No indication for the predicted strong concentration of the 1 g 9 2 strength in 207Pb is found.

Excitation of the giant resonance region in silicon by inelastic scattering of 115 MeV protons

Differential cross sections for the excitation of the giant resonance region in silicon have been measured over the angular range 10\ifmmode^\circ\else\textdegree\fi{} to 34\ifmmode^\circ\else\textdegree\fi{} by inelastic scattering of 115 MeV protons. The giant resonance exhibits fine structure which is similar to that observed in ($\ensuremath{\alpha}$,${\ensuremath{\alpha}}^{\ensuremath{'}}$) and low-energy ($p$,${p}^{\ensuremath{'}}$) data. The angular distribution for the giant resonance has been analyzed in terms of the distorted-wave Born approximation and 19-26% of the energy weighted sum rule strength for $L=2$ has been identified. It is also found that the angular distribution for the excitation of the giant resonance region cannot be explained by assuming only the presence of giant quadrupole resonance.NUCLEAR REACTIONS Si($p$,${p}^{\ensuremath{'}}$), $E=115$ MeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$ for giant-resonance excitations and the low lying levels. Calculated energy-weighted sum rule strengths.

Inner-hole excitations in89Zr and91Mo via the (3He, ) reaction at 97 MeV

The nuclei 89Zr and 91Mo have been investigated up to an excitation energy of about 25 MeV using the (3He, alpha ) reaction at 97.3 MeV incident energy. In addition to the well known low-lying levels and analogue states strongly excited groups of levels centered around 4.4 MeV are confirmed to belong to the 1f7/2 neutron inner shell in 89Zr, with a maximum of about 50% of the sum rule strength. A corresponding group, with comparable strength, is found for the first time in 91Mo at nearly the same excitation energy. In addition, and for both nuclei, two much smoother structures are observed lying under and beyond the analogue states. The authors discuss their possible attribution to the 1f7/2 T components respectively. Contributions from 1d inner shells are also considered. In both nuclei, new IAS fragments have been identified.

On the “missing” deep-hole strength in 115Sn

Evidence is found for a “new” deep hole component in 115Sn extending to about 18 MeV excitation and containing most likely 1 f 5 2 strength in addition to 2p strength. With this new component, a better definition of the “background” is possible. All of the combined 1 g 9 2 , 2 p 1 2 , 2 p 3 2 sum rule strength can be accounted for with the inclusion of the new component and the additional overall strength due to the reduced background.

The isoscalar strength distribution in 24, 26Mg, 28Si and 40Ca obtained from inelastic alpha scattering at 120 Mev

The inelastic α-scattering reaction at E α = 120 MeV with an energy resolution of 90–150 keV has been used to investigate isoscalar strength distributions in 24, 26Mg, 28Si and 40Ca. For 24, 26Mg and 28Si the E2 strength between E x = 14 and 27 MeV is strongly fragmented. In 40Ca the E2 strength is mainly concentrated near E x ~ 65 A 1 3 MeV, although here the onset of fragmentation can be observed. The sum rule strength for the different multipolarities was obtained by applying for each nucleus an L-dependent normalization procedure. In this way we observed in total in 24, 26Mg, 28Si and 40Ca for excitation energies up to 27 MeV an amount of (61 +8 −6), (50 +9 −8), (38 +8 −6) and (94 ± 14)%, respectively, of the isoscalar E2 energy weighted sum rule (EWSR) of which (36 +7 −5), (28 +8 −7), (24 +7 −5) and (74 ± 12)% was found between E x = 14 and 27 MeV. In addition isoscalar E0, E3 and E4 strength was observed in this excitation energy region. A detailed comparison has been made between the isoscalar quadrupole strength distribution observed in the 24, 26Mg(α, α') reaction and the E2 strength excitation function obtained from radiative α-capture measurements. In the low excitation energy region coupled channel effects have been observed, especially for the excitation of the 3 + states. Moreover, a considerable percentage of the 1ħω isoscalar dipole and octupole strength has been observed for excitations below 14 MeV.

New Giant Resonances in 172-MeVαScattering fromPb208

Spectra of 172-MeV ..cap alpha.. scattering from /sup 208/Pb indicate in addition to giant monopole and quadrupole excitation new giant resonance structures in hadron scattering at E/sub x/=17.5 +- 0.8 and 21.3 +- 0.8 MeV with corresponding widths of 4.8 +- 0.8 and 5.9 +- 0.8 MeV. The angular distributions indicate L=3 and 1 giving rise to an interpretation as isoscalar giant octupole resonance (17.5 MeVm 60% energy-weighted sum-rule strength), and isoscalar giant dipole resonance (21.3 MeV, 90% energy-weighted sum-rule strength).

Observation of the High-Energy Octupole Giant Resonance with 800-MeV Protons

Inelastic scattering of 800-MeV protons from $^{40}\mathrm{Ca}$, $^{116}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$ shows a broad giant resonance at an excitation energy of $\frac{110}{{A}^{\frac{1}{3}}}$ MeV. The angular distributions are consistent only with scalar-isoscalar $l=3$ transfer. The excitation energy and width of this high-energy octupole giant resonance are in reasonable accord with theory. However, its energy-weighted sum-rule strength (\ensuremath{\sim}20%) is only about one half that predicted by randomphase-approximation calculations.

Decay Modes of the Isoscalar Giant Quadrupole Resonance inNi58

Particle decay modes of the giant quadrupole resonance in /sup 58/Ni have been determined in a particle-particle angular correlation experiment. The branching ratios are (59 +- 12) % and (12 +- 4) % ((30 +- 6) % and (6 +- 2) % of the isoscalar E2 energy-weighted sum-rule strength) for proton and ..cap alpha..-particle decay, respectively, and are very similar to those of the underlying continuum and the statistical-model predictions. Our results disagree with a recent electroproduction singles experiment.

E0,E1,E2,E3, andE4giant resonances in theN=82nucleusCe140between 4 and 48 MeV excitation energy with inelastic electron scattering

The cross section for electron scattering from natural cerium (89% $^{140}\mathrm{Ce}$) has been measured with electrons of 80 and 92 MeV at 90 and 105\ifmmode^\circ\else\textdegree\fi{} between 4 and 48 MeV excitation energy. The nine resonances or resonance-like structures identified at ${E}_{x}=6(31{A}^{\ensuremath{-}\frac{1}{3}}), 7.4(38{A}^{\ensuremath{-}\frac{1}{3}}), 10(52{A}^{\ensuremath{-}\frac{1}{3}}), 12(62{A}^{\ensuremath{-}\frac{1}{3}}), 15.3(79{A}^{\ensuremath{-}\frac{1}{3}}), 22(114{A}^{\ensuremath{-}\frac{1}{3}}), 25(130{A}^{\ensuremath{-}\frac{1}{3}}), 31(160{A}^{\ensuremath{-}\frac{1}{3}})$, and $37.5(195{A}^{\ensuremath{-}\frac{1}{3}})$ MeV were classified on the basis of their momentum transfer dependence and discussed in the framework of the shell model. Since some of the arguments used are intricate we refer for quantitative particulars to the text. It is shown that the $E2$ sum rule strength not exhausted in the excitation range of this experiment may contribute up to 50% of the classical dipole sum rule to the photon cross section between 50 MeV and the pion threshold. The resonance at 10 MeV might be due to a separate oscillation of the excess neutrons against the rest of the nucleus.NUCLEAR REACTIONS $^{140}\mathrm{Ce}$($e$,${e}^{\ensuremath{'}}$, ${E}_{0}=50 \mathrm{to} 92$ MeV, Measured $\frac{{d}^{2}\ensuremath{\sigma}}{d\ensuremath{\Omega}d{E}_{x}}$, bound and continuum states (giant resonances). Deduced multipolarity, reduced matrix element $B(E\ensuremath{\lambda})$, radiative width ${\ensuremath{\Gamma}}_{y}^{\ensuremath{\circ}}$, sum rule exhaustion of giant resonances, photon cross section to pion threshold, total width of continuum and clustered states.

Giant-Resonance Studies with High-Energy Heavy Ions

Evidence is presented for the excitation of giant multipole resonances in inelastic scattering of 315-MeV $^{16}\mathrm{O}$ ions on $^{12}\mathrm{C}$, $^{58}\mathrm{Ni}$, and $^{208}\mathrm{Pb}$ targets. Highly excited modes around 20 MeV of excitation energy in $^{208}\mathrm{Pb}$ exhaust a large fraction of the energy-weighted isoscalar $E3$ and $E5$ sum-rule strengths.

Isoscalar Multipole Resonances inCa40

A correlation experiment between inelastically scattered /sup 3/He particles at 1.2/sup 0/ and decay ..cap alpha.. particles was performed in the giant-resonance region of /sup 40/Ca at an incident energy of 120 MeV. A new 0/sup +/ state with 6% energy-weighted sum-rule strength was observed at E/sub x/ = 14.2 MeV. Two broad resonances (quadrupole and possibly octupole) were observed at E/sub x/ approx. 18 MeV. No resonant structure was observed at E/sub x/ > 20 MeV.

Calculation of the spreading widths of the deep-lying hole states in the odd tin isotopes

The experimentally observed deep-lying hole states in (d, t) reactions on the even Sn isotopes are described in terms of a quasiparticle-phonon formalism. The fragmentation of the hole strength is calculated and subsequently the fragments are spread over the many underlying non-collective states in a statistical way. The results of the calculations are in qualitative agreement with experiment, in that the calculated structures are most pronounced for the lighter Sn isotopes. The fact that only a relatively small fraction of the total sum rule strength is exhausted experimentally in the gross structure peak cannot be explained by this Calculation.

The 116Sn(d, t) 115Sn reaction and the investigation of deeply bound hole states in the odd- A tin isotopes

Single-neutron pick-up via the (d, t) reaction was studied at E d = 50 MeV on all stable, even- A tin isotopes with an emphasis on the pick-up from the first major shell below the valence shell. The deeply bound hole states thus observed exhibit themselves as a gross structure phenomenon with a systematic variation of its width as a function of neutron number. The most extensive study was done for the 116Sn(d, t) 115Sn reaction for which angular distributions were obtained not only for the deeply bound hole states but also for the pick-up of valence nucleons, and for the excitation of the isobaric analogue states. A DWBA analysis yielded the full sum-rule strength for the pick-up of the valence nucleons. It located in the gross structure about 45% of the combined 1g 9 2 , 2p 1 2 , 2p 3 2 and 1f 5 2 strength. Additional strength may be found in the continuous “background” on which the gross structure peaks are riding. A systematic study of the gross structure shapes and cross sections in all odd- A tin isotopes is presented. The observed variation in the spreading of the 1g 9 2 hole strength as a function of neutron number is compared with recent calculations.

Deeply bound hole states and isobaric analog states in 89Zr

The 90Zr(τ, α) 89Zr reaction, at 39 MeV incident energy, was used to populate hole states up to 13.5 MeV excitation energy in 89Zr. A split-pole spectrometer was used for particle analysis and detection. In the excitation energy range between 0 and 3.5 MeV, about twenty well-resolved states were observed in 89Zr, many for the first time. These states contain almost all of the spectroscopic strengths of the 1g 9 2 , 2p 1 2 , 2p 3 2 and 1f 5 2 neutron Subshells. The 30–35 keV energy resolution of the present study revealed a fine structure in the bump previously observed around 4.5 MeV and tentatively identified as the main part of the 1f 7 2 . hole orbital. About thirty levels or groups of levels were excited between 3.5 and 7.0 MeV excitation energy and angular distributions have been extracted for each individual group as well as for the gross structure itself. A DWBA analysis of the data was carried out and shows that the main part of the observed fine structure is populated by l = 3 angular momentum transfer. The full sum rule strengths obtained for the states below 3.5 MeV for the pick-up of the 1g 9 2 , 2p 1 2 . 2p 3 2 and 1f 5 2 nucleon lead to the identification of this highly fragmented bump with the 1f 7 2 shell. We found between 50 to 70 % of the 1f 7 2 hole strength in this region. Four sharp and strongly excited peaks are observed at higher excitation energy (8–10 MeV) above a continuous background. They are identified with the known isobaric analog states of the first four excited levels in the 89Y parent nucleus. Around 13 MeV a weakly excited peak is observed which has an l = 3 angular distribution. This level is proposed as the IAS of the first component of the 1f 7 2 . proton hole orbital located around 5 MeV in 89Y. In order to compare the spectroscopic strengths of the IAS and of their parent states, the neutron form factor has been calculated by solving the Lane coupled-channel equations. This method is shown to produce an overall agreement between the strengths of the parent analog pairs of levels.

Observation of a Low-Energy Octupole Resonance in Medium-Mass Nuclei

A giant-resonance-like structure at ${E}_{\mathrm{exc}}\ensuremath{\sim}\frac{32}{{A}^{\frac{1}{3}}}$ MeV is observed in ($\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}}$) spectra in nuclei from $^{90}\mathrm{Zr}$ to $^{154}\mathrm{Sm}$. Analysis of the angular distributions leads to an assignment of ${J}^{\ensuremath{\pi}}={3}^{\ensuremath{-}}$ and an energy-weighted sum-rule fraction of 16-22% for this structure. Comparison with random-phase-approximation calculations shows that $\ensuremath{\sim}\frac{2}{3}$ of the expected $1\ensuremath{\hbar}\ensuremath{\omega}$ octupole energy-weighted sum-rule strength is found at $\ensuremath{\sim}\frac{32}{{A}^{\frac{1}{3}}}$ MeV; the remainder occurs in low-lying ${3}^{\ensuremath{-}}$ states.

Isoscalar multipole strength inMg24through inelastic alpha scattering

Inelastic $\ensuremath{\alpha}$ scattering was studied on $^{24}\mathrm{Mg}$ at 70 MeV $\ensuremath{\alpha}$ energy. With an over-all resolution of 70-100 keV 40 distinct peaks are seen in energy spectra below 16 MeV excitation. The experimental angular distributions for individual peaks were analyzed in terms of the distorted wave Born approximation to extract transition strengths. About 50-70% of the quadrupole energy-weighted sum rule strength is observed up to 19 MeV excitation. Though there is a slight peaking of $l=2$ strength around 16 MeV excitation it is found to be spread over a broader (\ensuremath{\sim} 10 MeV) energy range than is the case (typically 5-6 MeV) for heavier ($Ag40$) nuclei. Up to 16 MeV the observed strength for the octupole vibrations is 10% of the energy-weighted sum rule and it is consistent with that estimated to reside around $1\ensuremath{\hbar}\ensuremath{\omega}$ excitation. Only 3% of the $l=4$ energy-weighted strength is seen below 16 MeV.NUCLEAR REACTIONS $^{28}\mathrm{Mg}(\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}})$, ${E}_{\ensuremath{\alpha}}=70$ MeV, ${E}_{\mathrm{excitation}}=0\ensuremath{-}30$ MeV; measured $\ensuremath{\sigma}({E}_{{\ensuremath{\alpha}}^{\ensuremath{'}}},\ensuremath{\theta})$ deduced quadrupole, octupole, and hexadecapole strength by DWBA and compared with sum rules. Enriched target.