Experimental study onp-wave neutron strength functions for light nuclei

Broad energy distributions in fast neutron beams have been achieved by appropriate filtering of the²³⁶U fission radiation provided from the RENT converter facility at the FRM research reactor. Transmission measurements in such beams result in average cross sections to which resonance reactions and shape elastic scattering contribute. We used a silicon (124.5 cm) filtered beam with a median energy of 143 keV (width 20 keV) and beams with 1.3 MeV (0.55 to 3 MeV) and 2.1 MeV (1 to 5.5 MeV) obtained through different filter combinations of lead and polyethylene. The relative high energies and the broad spectra made it possible to determine experimentally the contributions ofs- andp-wave resonance reactions to the average cross section even for light nuclei. Using the three different beams we determined the average cross sections for the elements in the mass regionA=9 to 65. Analysing the measured cross sections by means of theR matrix formalism provided a complete set ofp-wave strength functions and distant level parameters. Moreover, single particle shell effects in the cross sections were observed. In conclusion we obtained informations on the 2P and the 3S size resonances and about the validity of the optical model for neutron reactions with light nuclei.     

Neutron strength functions of nuclei in the deformed region

P-wave neutron strength functions of 21 nuclei, in the rare-earth and deformed region 138 <A < 202, have been extracted from the average capture cross sections measured using SbBe photoneutrons and activation technique. S-wave neutron contribution is computed using the s-wave resonance parameters available in literature and subtracted out from the measured total capture cross section to yield the p-wave neutron capture contribution from which the p-wave neutron strength functions are extracted. Present results are found to be in general agreement with the values reported in literature. The experimental p-wave neutron strength functions are also compared with the theoretical predictions based on the different versions of the optical model potential, and qualitative agreement is observed with the deformed optical model theory of Buck and Perey. Strong evidence for shell structure effects is also noticed.     

Analysis of average primary gamma-transition intensities and cross sections of the113Cd(n, γ) reaction

A combined analysis of the available data on the primaryγ-ray intensities from the¹¹³Cd(n, γ) reaction atE _n=1.9 and 24.3 keV neutron energies together with the data on¹¹³Cd neutron capture cross sections in theE _n=3–200 keV energy region was carried out. The neutron strength functions were determined asS _n0=(0.260±0.073) 10^?4 and S_n1=(5.06±0.67) 10^?4. No spin-orbit splitting of thep-wave neutron strength function was found. The energy dependence of theE 1 radiative strength function {ie147-01} was fitted by the Kadmenski-Furman model somewhat better than by a standard Lorentzian. TheM 1 giant resonance parameters were obtained as E _G ^{M 1} =8.8±1.6 MeV and Γ _G ^{M 1} = 4.7±2.6 MeV. The neutron capture cross section of¹¹³Cd from its isomeric state ({ie147-02}=11/2^?, E ₁ ^m =263.7 keV) was calculated.     

Optical model calculation for neutron capture in the mass region A=40–70

Calculations of thes, p andd-wave neutron strength functions based on the spherical optical model have been performed for the mass region A=40–70. The aim was to investigate the radiative neutron capture observed in this region leading to final states with spin J=5^?/2 and J=7^?/2. Results of the calculation indicate thatd-wave neutron capture followed by E1 radiative decay is the most likely explanation of the process.     

Virtual excitation of the GDR mode in the subbarrier23Na(p, γ)24Mg reaction

Differential cross sections for nonresonant radiative capture of low energy protons (E _p = 1,348 keV and 1,370 keV) by²³Na nuclei exhibit features pointing to the virtual excitation of the giant dipole resonance (GDR) mode. Theoretical analysis carried out within the framework of the direct — semidirect capture model reveals an enhanced coupling of the GDR with the incident protonf-wave consistent with the microscopic structure of the GDR in thes-d shell nuclei.     

Shell model study of high spin states in theN=50 nucleus93Tc

High spin states in theN=50 nucleus⁹³Tc were reinvestigated by using the reaction⁶⁴Zn (³⁵Cl,4p 2n) at a beam energy of 140 MeV. This was done particularly with a view to observe anyγ rays upto 2.7 MeV which may have been missed in our earlier study where the experimental conditions were set to observeγ rays upto 2 MeV. We found four newγ rays of energy: 2484, 2164, 2130 and 69 keV. We have placed theseγ rays in the level scheme and it now gets extended to 49/2^?. Though there is no substantial change in the level scheme, placing theγ rays in the level scheme has resulted into two important conclusions: (1) We have performed shell model calculations for⁹³Tc nucleus within a model space which encompasses an enlarged proton configuration and allows for the excitation of the neutron across theN=50 core. The excitation of a single neutron across theN=50 core satisfactorily explains the new level scheme. (2) The energy of the 17/2^? isomeric state is now unambiguously placed at 2185 keV.     

s- and p-wave neutron spectroscopy Xc. Intermediate structure: 88Sr

Neutron total cross section measurements of natural Sr were made from 50–875 keV using a high resolution proton beam and the ⁷Li(p, n) reaction as a neutron source. These data were analyzed with the help of an R-Matrix code to extract resonance (energies and other) parameters up to about 850 keV. 2p-1h and particle-vibration doorway interpretation of the s-, p- and d-wave resonances is attempted in terms of the sum rule Σγ_n² = γ_d². Predictions based on both of these models agree with the experimental results. As expected the p-wave resonances are stronger than either s- and d-wave structure. Theory accounts for the p-wave strength remarkably well. Possible location of the p-wave s.p. resonance is reproduced with a real potential and its damping due to the imaginary potential is calculated.More fragmentation of the strong p-wave doorways is observed than was expected for a compound nucleus so near ⁹⁰Zr, but a larger strength function is observed apparently due to the p-wave giant resonance.     

Search for missing predicted high-spin states in28Si

New shell model calculations have predicted several high-spin (I ^π=5⁺ and 6⁺) levels in²⁸Si near 10 MeV excitation energy which are missing from or ambiguous in existing experimental studies. Angular distributions, linear polarizations and Doppler-shifts ofγ-rays have been measured for theγ-decay of theE _p=1,911 and 2,073 KeV resonances of the²⁷Al(p, γ) reaction in an attempt to discover these missing states or confirm the discrepancies between experiment and theory. The excitation energies and spin-parities of the resonances were determined as 13,424.4±0.2 keV,I ^π=5⁺ and 13,582.3±0.5 keV,I ^π=6⁺. States populated in theγ-decay of these resonances were assigned spins and parities as follows: 11,777 keV,I ^π=5⁺; 11,331 keV,I ^π=6⁺; 10,417 keV,I ^π=5⁺; 9,417 keV,I ^π=4⁺ and 8,945 keV,I ^π=5⁺. On the basis ofγ-ray transition rates T=1 is assigned to the 13,424 keV level and T=0 to the 10,417 and 11,777 keV levels. With the new data excellent agreement is achieved between the experimental spectrum of²⁸Si and the new shell model predictions. These data provide evidence for aK ^π=3⁺ rotational band comprised by the 6,276, 6,889, 8,945 and 11,331 keV levels. This band emerges also from the shell model wave functions as do theK ^π=0⁺ bands based on the ground state and the 6,691 keV state.     

s- and p-wave neutron spectroscopy Xf(i). Intermediate structure in the 28Si + n reaction: R-matrix interpretation of experimental data

A multilevel R-matrix analysis of Si neutron cross-section data measured at NBS has been performed up to about 4.5 MeV neutron energy. Only a small fraction of the p- and s-wave s.p. strength is observed, but both exhibit local concentrations of strength indicative of doorway structure around 1 and 0.2 MeV, respectively. Besides the well-known 180 keV, strong, $\text{1}\text{2}{}^{\mathrm{+}}$ resonance, the s-wave resonance structure is of moderate strength and widely distributed. The f- and d-wave assignments are not unambiguous, but J > 3/2 resonances show strong signs of intermediate structure for d-waves. A possible correlation between neutron and gamma decay channels and the connection between the states observed in (n, n), (d, p), (n, γ), and (γ, n) channels is discussed. A coreparticle doorway interpretation for s and p- waves is presented.     

The cross section of14N(n,p)14C at stellar energies and its role as a neutron poison forS-process nucleosynthesis

The absolute average cross section 〈σ〉 of the¹⁴N(n, p)¹⁴C reaction has been measured using neutron spectra that closely resemble Maxwell-Boltzmann distributions with thermal energies of kT=25.0 and 52.4 keV: 〈σ〉=0.81±0.05 and 0.52±0.06 mb, respectively. The resulting reaction rates are nearly the same at T₉=0.29 and 0.61, and their average, N_A〈συ〉=(1.3±0.1)×105 cm³ s^?1 mol^?1, is about a factor of three smaller than the previously adopted values obtained by extrapolation between thermal and higher-energy data. Thus, the¹⁴N(n, p)¹⁴C reaction plays a correspondingly smaller role as a neutron poison fors-process nucleosynthesis.     

Study of the36Cl(n,p)36S reaction in the neutron energy range up to 10 keV

The³⁶Cl(n,p)³⁶S reaction cross-section was measured by the time-of-flight method in the IBR-30 pulsed reactor of the JINR. The measured cross-section shows three not previously observed neutron resonances with energies E_n = 1.3; 3.5 and 8.2 keV for which the parameters A_p=gΓ_nΓ_p/Γ: 0.07 ±0.01; 0.08 + 0.03 and 1.7 + 0.3 eV were determined, respectively. Comparison of these results with the excited states obtained by the³⁶S(p, γ)³⁷Cl reaction made possible a more exact determination of the scale energy of the³⁷Cl nucleus excited states.     

IsoscalarE2 transition strengths in 10≦A≦48 nuclei

Electric quadrupole transition strengths for the 2 ₁ ⁺ ,T=1→0 ₁ ⁺ ,T=1γ-decay branches are summarized for 10≦A≦42 nuclei. In¹⁰B the corresponding branch has been remeasured by use of the⁹Be(p, γ)¹⁰B resonance reaction atE _p =320 keV; an upper limit of 0.6% is found. The variation of theE2 strengths within each individualT=1 isobaric multiplet reveals the particleor hole-character of the levels involved. The isoscalar 2 ₁ ⁺ →0 ₁ ⁺ transition strengths in 10≦A≦48 nuclei vary between 2 and 20 Weißkopf units showing drastic shell effects. Results for the ratio of neutron and proton matrix elements deduced from analogγ-decay studies and from inelastic pion scattering are compared.     

Statistical model calculations for medium and strong absorption in theA=90 region

Calculations of elastic, inelastic and total neutron cross sections as well as of (p, n) reaction cross sections in theA=90 mass region have been performed, using the statistical model of Hofmann, Richert, Tepel and Weidenmüller. The optical model parameters were obtained by Finckh et al. from the neutron decay of IAR in the⁹¹Zr(p, n)⁹¹ Nb reaction. The calculations are in very good agreement with the published experimental data. The optical model parameters proved to be satisfactory up to aboutE _n=8.0 MeV. The present work might be relevant to the evaluation of neutron data for reactor technology.     

High-spin states in27Al

The²⁴Mg(α, p γ) reaction has been studied atα-particle energies of 13, 15, and 15.2 MeV. Using method II of Litherland and Ferguson spin assignments or restrictions thereof could be made to the²⁷Al levels atE _x =5500 keV (I=11/2, 7/2), 6950 keV (I=11/2, 7/2), 7226 keV (I=9/2), 7286 keV (I=9/2–13/2), 7399 keV (I=11/2, 7/2) and 7443 keV (I=13/2, 9/2). Using the Doppler-shift attenuation method a lifetimeτ=20–50 fs was obtained for theE _x =7399 keV level and a limitτ<20 fs for the levels atE _x =7443, 7286, 7226, 6950, 6718, and 6287 keV, respectively. Further spin assignments in²⁷Al were obtained by a study of the²⁶Mg(p, γ) reaction at the E_p=2174 keV resonance. Fromγ-ray angular distributions the resonance spin was determined as I=9/2 (previous assignmentI=7/2) and the spin of theE _x =5959 keV level was determined asI=7/2. Tentative spin assignments were made to the levels atE _x =6537 keV (I=7/2) and 6718 keV (I=9/2). From the combined evidence of the²⁴Mg(α, p) and²⁶Mg(p, γ) reactions the spin of the 6287 keV level was found to beI=7/2. The results are compared with shell model calculations and the Nilsson model.     

Derp 3/2-Analogzustand in51V

In an investigation ofT=7/2 analogue states in⁵¹V the⁵⁰Ti(p, γ) excitation curve has been measured for proton bombarding energies 1280–1480 keV and 2340–2660 keV. From the (p, γ) resonances 29 new virtual levels in the region of 9316–9510 keV excitation energy in⁵¹V were determined. The strong resonance atE _p=1 371 keV has been identified as the isobaric analogue state of the⁵¹Ti ground state by determining spin and parity of this resonance to be 3/2^?. There is no evidence for a strong analogue resonance in⁵¹V corresponding to the 1.16 MeV _{p 1/2} state in⁵¹Ti. The γ-decay of the _{p 3/2} analogue state has been studied by measuring branching ratios and angular distributions of primary γ-transitions with a Ge(Li) detector.M1E2 mixing ratios have been determined for these transitions. The total width of the resonance for γ-decay is found to be Γ_γ=1.6±0.4 eV. New bound levels in⁵¹V have been introduced at 3576, 4651 and 4661 keV excitation energy. TheJ ^π values of the 3085, 4770, and 4863 keV states are determined to be 5/2^?, 5/2^?, 3/2^?, respectively. The analogue-antianalogueM1 transition strength is found to be considerably reduced compared to the situation ins-d shell nuclei.     

Winkelverteilung und Wirkungsquerschnitt der Reaktion6Li(p, α)3He im Energiebereich von 50 bis 190 keV

In the angular distribution 1+A ¹ cos ?+A₂cos²? of the³He particles (cm. system)A ₁ decreases from +0.152±0.018 at 188 keV to ?0.017±0.023 at 62 keV. The slope of the A₁-curve is not approaching zero in this energy range, thereby showing the participation of terms of opposite parity even at very low energies. The total reaction cross section deviates from ans-wave Gamow-plot above appr. 130 keV, being 10 mb at 130 keV. The experimental results are discussed in connection with suggested level diagrams of the compound nucleus⁷Be.     

Proton states in143Pm and145Pm populated in the (3He,d) reaction

The (³He,d) reaction on targets of¹⁴²Nd,¹⁴⁴Nd and on a target of natural Nd have been studied, using a beam of 24 MeV³He from the McMaster University Tandem Van de Graaff accelerator. The reaction products were analyzed with an Enge type magnetic spectrograph and recorded on photographic emulsions. Information on thel-values was obtained from the (³He,d) angular distribution. In the¹⁴³Pm nucleus no fragmentation of the shell model strength was found while in the¹⁴⁵Pm nucleus the fragmentation of thed _3/2 ands _1/2 states was significant, giving a total of 11l=2 and 51=0 transitions. The results are analyzed in terms of the spherical shell model and the agreement with pairing theory is excellent in both cases. A survey of the stripping strength to promethium isotopes with mass numbers ranging fromA=143 toA=151 is presented, using normalizations based on the results from the experiments on the target of natural neodymium.     

Neutron radiative capture in Cu

Radiative neutron capture in natural Cu has been studied in the neutron energy range from 200 eV to 16.5 keV. An area analysis of the data yields information on resonance parameters: For large resonances (Γ _n ?Γ _γ ) with known isotopic assignments values ofΓ _γ or, if the spin of the resonance is unknown, 2g Γ _γ are obtained. In some cases, it was possible to assign the spin of the resonance from the measured 2g Γ _γ assuming a fairly constant radiation width. For a number of small resonances (Γ_n?Γ _γ ) with unknown isotopic assignment, values of 4agΓ _n (a=isotopic abundance) have been determined. The distribution of these values, including those of the stronger resonances known from literature, shows an excess of small widths which is attributed top-wave levels. From this, thep-wave neutron strength function for natural Cu is estimated to be $$S_1 = \left( {0.30_{ - 0.14}^{ + 0.18} } \right)10^{ - 4} $$ .     

Structure of28Si from the spectroscopy of high-spin states

A search for high-spin states in²⁸Si has been performed byn?y coincidence measurements in the²⁵Mg(α,nγy) reaction atE _α=14 and 15.5 MeV. Spin-parity assignments of the observed levels were obtained fromn?γ angular correlation and lifetime measurements atE _α=14.5 MeV. Theγ-decay of the 9,164 keV level was investigated separately with the²⁷Al(p, γ) reaction at theE _p=2,160 and 2,312 keV resonances. Rotational bands withK ^π=3^? (comprising levels atE _x=6,879, 8,413, 10,188 and 12,204 keV),K ^π =5^? (comprising levels atE _x=9,702, 11,577 and 13,741 keV) andK ^π=0⁺ (comprising levels atE _x=6,691, 7,381, 9,164 and 11,509 keV) were observed. The finding of the latter band supports the idea of coexisting oblate and prolate shapes in²⁸Si. A level at 14,643 keV excitation energy has the properties of theI ^π=8⁺ member of the ground state band. There are additional positive-parity high-spin states which do not fit into rotational bands. All types of positive-parity states are well accounted for by shell model calculations.     

Destruction of26Al in explosive nucleosynthesis

The²⁶Al(n, p)²⁶Mg reaction has been studied using neutron spectra which closely resembled Maxwell-Boltzmann (M.-B.) distributions with thermal energies ofkT=40 ×10^?6, 31 and 71 keV and also forE _n =270–350 keV. These energies correspond to stellar temperaturesT ₉=4.6×10^?7, 0.36, 0.82 and 3.1–4.1, whereT ₉ is in units of 10⁹ K. The partial cross sections for thep ₀-(p ₁-)transition are found to equal 26±10(1,850 ±150), 13±6(124±17), 16±13(84±14) and 21±8(72±15) mb for the above neutron spectra, respectively. The astrophysical reaction rate is determined for the combinedp ₀- andp ₁-transitions to beN _A 〈σν〉=(0.324±0.026, 20.5±2.7, 22.6±4.3 and 38.7±11.1) ×10⁶ cm³ mole^?1 s^?1. The results are compared with previous investigations and with statistical model calculations.