Inelastic Α-scattering Research Articles

Testing the mutually enhanced magicity effect in nuclear incompressibility via the giant monopole resonance in the 204,206,208Pb isotopes

Using inelastic α-scattering at extremely forward angles, including 0°, the strength distributions of the isoscalar giant monopole resonance (ISGMR) have been measured in the 204,206,208Pb isotopes in order to examine the proposed mutually enhanced magicity (MEM) effect on the nuclear incompressibility. The MEM effect had been suggested as a likely explanation of the “softness” of nuclear incompressibility observed in the ISGMR measurements in the Sn and Cd isotopes. Our experimental results rule out any manifestation of the MEM effect in nuclear incompressibility and leave the question of the softness of the open-shell nuclei unresolved still.

Giant monopole resonance in even-A Cd isotopes, the asymmetry term in nuclear incompressibility, and the “softness” of Sn and Cd nuclei

The isoscalar giant monopole resonance (ISGMR) in even-A Cd isotopes has been studied by inelastic α-scattering at 100 MeV/u and at extremely forward angles, including 0°. The asymmetry term in the nuclear incompressibility extracted from the ISGMR in Cd isotopes is found to be Kτ=−555±75 MeV, confirming the value previously obtained from the Sn isotopes. ISGMR strength has been computed in relativistic RPA using NL3 and FSUGold effective interactions. Both models significantly overestimate the centroids of the ISGMR strength in the Cd isotopes. Combined with other recent theoretical effort, the question of the “softness” of the open-shell nuclei in the tin region remains open still.

Measurement of neutron-skin thickness in 208Pb by excitation of the GDR via inelastic α-scattering

The neutron-skin thickness in 208Pb was determined by measuring the cross section of the isovector giant dipole resonance (GDR) in inelastic scattering of 196 MeV α-particles. From the comparison of measured and calculated cross sections the relative difference of proton and neutron distribution radii (ΔR pN /R 0) was deduced to be 2.2 ± 1.2%.

Isoscalar giant dipole resonance in [formula omitted]Pb via inelastic α scattering at 400 MeV and nuclear incompressibility

The isoscalar giant dipole resonance (ISGDR) in 208Pb has been investigated with inelastic α-scattering of 400 MeV at extremely forward angles, including 0°. Energy spectra, virtually free from instrumental background, have been obtained and the ISGDR strength distribution has been extracted using a multipole-decomposition analysis (MDA). A difference-of-spectra approach yields the same ISGDR centroid energy as with MDA. These results lead to a value for nuclear incompressibility that is consistent for both the isoscalar dipole and monopole modes.

Investigation of inelastic α-scattering on 24Mg and 28Si

Effects of three different α-nucleus potentials, the normal Woods-Saxon (WS), the squared WS and the molecular, have been studied using the differential cross-section data of inelastically scattered α-particles on 24Mg and 28Si at 54 and 26 MeV incident energies, respectively. The angular distributions of inelastic scattering to the first 2+ and 4+ states of the two nuclei have been analyzed in terms of a coupled-channel formalism. The macroscopic rotational model using both the squared WS and the molecular potentials can produce satisfactorily a simultaneous description of the elastic data and the inelastic-scattering data of the 2+ and 4+ states for both the targets. The normal WS potential fails to describe the elastic and inelastic data, simultaneously. The effects of second-order deformed potential are also investigated. Microscopic coupled-channel calculations, using the 0+-2+ coupling and the Gaussian α-nucleon interaction in the form-factor, have also been performed for the 28Si target using both the squared WS and molecular potentials, the latter one giving a reasonable description of the data.

Excitation of the isovector GDR by inelastic α-scattering as a measure of the neutron skin of nuclei

The cross section of the isovector giant dipole resonance (GDR) has been measured in the 116,124Sn(α, α′γ 0), 150Nd(α, α′γ 0) and 208Pb(α, α′γ 0) reactions at E α = 120 MeV and 0° ⩽ Θ α′ ⩽ 3°. The results are compared with DWBA calculations performed with nuclear GDR form factors that depend on the relative difference between the radii of proton and neutron distributions ( ΔR PN/ R 0). Taking a linear combination of form factors provided by the Gold-haber-Teller and Steinwedel-Jensen models in a ratio that fits the GDR systematics, the ΔR PN values for 116Sn, 124Sn and 208Pb were deduced by comparing measured and calculated cross sections to be 0.02 ± 0.12 fm, 0.21 ± 0.11 fm, and 0.19 ± 0.09 fm, respectively. For the deformed 150Nd, the neutron-skin thickness along and perpendicular to the symmetry axis was found to be 0.22 ± 0.16 and 0.50 ± 0.15 fm, respectively, yielding β n 2/ β p 2 = 0.92 ± 0.08.

Radial excitation of the P11(1440 MeV) resonance and the compressibility of the nucleon

The excitation of P11 resonance N(1440) is investigated in inelastic α-scattering on hydrogen using α-particles from Saturne with a beam momentum of 7 GeV/c. In the missing mass spectra of the scattered α-particles two effects are observed, excitation of the projectile, preferentially excited to the Δ resonance, and excitation of the Roper resonance. The large differential cross sections indicate a structure of a compression mode from which the compressibility of the nucleon KN is deduced to be 1.4 ± 0.3 GeV.

Elastic and inelastic scattering of 30 MeV α-particles on even isotopes of palladium

Differential cross sections for elastic and inelastic α-scattering on 104Pd, 106Pd, 108Pd and 110Pd have been measured at E α = 30.5 MeV. The analysis of the elastic scattering has been performed with Woods-Saxon potentials, leading to a set of mean optical-model parameters. Coupled channels calculations including the most prominent low-lying excited states confirm collective vibrational excitations. The extracted quadrupole and octupole transition matrix elements are compared to existing electromagnetic data.

Nucleon scattering analysis from90,92,594Zr and isospin decomposition of transition matrix elements for low-lying collective transitions

Simultaneous analysis of neutron and proton inelastic scattering to low-lying collective states in90, 92, 94Zr are used to derive an isospin decomposition of the corresponding transition matrix elements. The deduced (M n/Mp) ratios for the strongest transitions are in sharp disagreement with values derived from Coulomb-nuclear interference observed in 35.4 MeV inelastic α-scattering from even Zr isotopes.

Inelastic α-scattering from 90Zr and 96Zr

The 90Zr and 96Zr(α, α') reactions have been studied at 35.4 MeV with an energy resolution of 35–50 keV. Angular distributions were measured between 10 and 50 degrees for an E x range of 1.5 to 6.0 MeV. Spin assignments have been made on the basis of the shapes of the differential cross sections and by comparison with collective DWBA calculations. For 96Zr discrepancies in spin assignments have been removed for several levels. Within the framework of the vibrational model isoscalar transition rates have been derived.

Fission decay of the isoscalar giant quadrupole resonance in 24Mg

The 24 Mg(α, α′) 12 C+ 12 C reaction was studied by measuring 12C fragments in coincidence with inelastically scattered α-particles at E α = 120 MeV. Both 12C fragments were identified using the ΔE − E technique. The measured angular correlations indicate that the 12C gs+ 12C gs decay channel is dominated by decay of L = 2 strength, which yields an integrated fraction of 0.14% of the E2 EWSR strength in comparison with 22.2% of the E2 EWSR strength observed in singles inelastic α-scattering experiments in the same excitation energy region.

Inelastic α-scattering to the continuum: A probe of α-clustering in nuclei

The statistical multistep direct theory is applied to the 90Zr(α, α′) reaction at 140 MeV. Using the averaging procedure already tested in (p, n) and ( p , p′0) reactions, DWBA matrix elements are employed to construct both the single-step and multistep cross sections in the continuum. It is shown that good fits for angular distributions in the 10–60 MeV excitation range can be achieved only by taking into account the interaction of the incoming α-particles with preformed α-particles in the target nucleus. By comparing both the shape and absolute value of cross sections with data, an α-clustering probability is extracted which is shown to be in agreement with independent analysis in the same mass region. Due to its surface localization, the possible role of inelastic α-scattering in the 100 MeV region to investigate α-clustering in nuclei is suggested.

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.

Experimental and theoretical study of line shapes in 13C(α, α′) inelastic scattering to resonant states

The line shape of the J π = 3 2 +, E x = 7.677 MeV resonance in 13C excited by inelastic scattering of α-particles is measured. It shows an asymmetric line shape with a dip on the high-energy side of the resonance. This is in contrast to the line shape of that resonance as seen in the 12C(n, n) 12C elastic scattering and the corresponding 12C(d, p) 13C reaction, where the dip is on the low-energy side. The asymmetric line shape in the inelastic α-scattering which can be parametrized by a (complex) parameter q is explained theoretically as the interference of a continuum transition and the excitation of a quasibound configuration, in close analogy to the analysis by Fano of asymmetric line shapes in inelastic electron-atom scattering. The line shape parameter q is sensitive to nuclear models and thus is a new tool in the study of nuclear wave functions.

Strong coupled-channels effects in the 9Be(α, t) 10B reaction

Differential cross sections were measured for the reactions 9 Be(α, α') 9 Be, 9 Be(α, t) 10 B and 9 Be(α, 3 He) 10 B at E α = 65 MeV for angles ranging from θ lab = 6° to 48°. Optical-model analysis was performed for elastic α-scattering from 9Be at E α = 48, 65 and 104 MeV, and DWBA and CC calculations were done for the inelastic α-scattering at E α = 65 MeV. DWBA calculations for the 9Be(α, 3He) reactions do not fit the transfer data so well and extracted spectroscopic factors are in disagreement with those of Cohen and Kurath and with values obtained from other reactions. Full CRC calculations assuming a band structure for the low-lying states of 10B and employing a modified set of Cohen and Kurath spectroscopic factors yield globally better fits both in shape and in absolute cross section for differential cross sections to low-lying states in 10B obtained in 9Be(α, t) 10B at E α = 65 MeV and 9 Be( 3 He, d) 10 B at E d = 17 MeV . In general, strong coupled-channel effects mainly affecting the distorted waves are observed both in entrance and exit channels.

A study of the giant resonance region of 40Ca by inelastic scattering of 104 MeV α-particles

Inelastic α-scattering experiments have been performed on 40Ca at E α =104 MeV in the angular range θ lab=4°– 16°. From the angular distributions of the giant resonance structures in the excitation energy region E x=13.3–21.8 MeV the contributions of different L-transfers have been determined.

Isoscalar excitations in the lead region observed in inelastic α-scattering at Eα = 120 MeV

Inelastic α-scattering from 197Au, 206Pb, 208Pb and 209Bi has been measured at an α-bombarding energy of 120 MeV. In the giant resonance region an isoscalar resonance (GR2) at E x ∼ 80A − 1 3 , in addition to the well-known GQR resonance (GR1) at E x ∼ 63 A − 1 3 , is observed. DWBA calculations were performed with the collective form factor prescription. The angular distribution of the GQR bump is found to be better fit if a small admixture of 20 % of the E4, energy-weighted sum rule (EWSR) is added to ∼ 100 % of the E2, EWSR. The angular distribution of the higher bump (GR2) is well fit both with an L = 2 and L = 0 transfer in our angular range. If it is L = 0, it then exhausts 100 % of the monopole EWSR. Angular distributions to low-lying states in 208Pb were also obtained. DWBA calculations with collective form factors were performed to fit these data. Around 33 %, 15 % and 7 % ofE3, E4 and E5 EWSR's are exhausted in these low-lying transitions in addition to the 15 % E2, EWSR in the 2 + state at 4.10 MeV.

Excitation of ground and gamma bands in the 24Mg(α, α') 24Mg reaction at 120 MeV

The cross sections for excitation of the members of the ground state (g.s.) band 0 −(g.s.), 2 + (1.37 MeV) and 4 + (4.12 MeV) and the γ-band 2 + γ (4.24 MeV), 3 γ +(5.24 MeV) and 4 γ +(6.01 MeV) in 24Mg have been measured in inelastic α-scattering at E α = 120 MeV. The excitation of these states are found to be well described by a coupled-channel calculation (CCBA) performed in the framework of the asymmetric rotational model. Two sets of parameters are found to give excellent fits to the data, but in both a direct coupling between the ground state and the 4 + state is found necessary.

Alpha-particle inelastic scattering form factors in the Coulomb-nuclear interference region

Alpha-particle scattering cross sections have been measured at 15, 18 and 19 MeV from the ground state and first excited state of 52Cr, 56Fe, 60Ni and 64Zn. Excitation functions have also been measured for inelastic α-scattering from 52Cr and 60Ni. The data extends into the forwardangle Coulomb-nuclear interference region. The results are analysed with the optical model and DWBA, using the deformed potential model. The relative and absolute magnitudes of the nuclear and Coulomb deformation parameters and the shapes of the form factors have been deduced from the data. The importance of data in the Coulomb-nuclear interference region in determining these quantities is demonstrated.

Octupole-strength concentration observed in α-scattering on 27A1

Angular distributions for inelastic α-scattering on 27A1 were measured at E α = 145.0 MeV. The data were analyzed for excitation energies less than 14 MeV. A strong group of levels with maximum intensity around 7.2 MeV excitation energy having a bell-shape like envelope with a FWHM of about 4 MeV was observed. The group shows strong octupole strength as deduced by comparison of the experimental results to DWBA calculations.