Giant spin-isospin vibrations and the continuum spectra from the (p,n) reaction at forward angles

The giant Gamow-Teller (GT) resonance and the spin-isospin multipole vibrations are calculated in terms of the continuum RPA. The effective particle-hole interaction consists of the Migdal parameter $\text{g′ = 0.7 (}\text{in units of}\text{?;}{}^2\text{μ}{}_{\mathrm{\pi }}{}^2\text{≈390}\text{MeV}\text{·}\text{fm}{}^3\text{)}$ and the one-pion exchange potential. The RPA response functions are obtained within the full 1p-1h space. In addition to the natural escaping width of the single particle, a constant spreading width for 1p-lh states is incorporated into the correlation function, which makes numerical calculations fast and feasible. The giant GT resonances in ⁹⁰Zr and ²⁰⁸Pb collect, respectively, about 80% and 93% strengths of the sum-rule limit within the nucleon degrees of freedom. It is found that the strengths are further quenched by about 30% due to the coupling with the isobar Δ(1230)-hole configuration. The total quenching thus amounts to 0≈45% and ≈40% respectively in two cases, which is in fair agreement with experiment. The continuum cross section of the ⁹⁰Zr(p, n) reaction at forward angles are calculated for spins up to J = 4 with both parities in the distorted-wave Born approximation. While the giant GT resonance is located at a low excitation energy $\text{h}\text{?}\text{ω ≈ 17}\text{MeV}$, the broad peaks of the dipole and quadrupole modes are found to dominate at $\text{h}\text{?}\text{ω ≈ 25}\text{and}\text{35}\text{MeV}$, respectively. The calculation fairly reproduces the experimental inclusive cross sections up to $\text{h}\text{?}\text{ω ≈ 50}\text{MeV}$.     

Core polarization for M2 transitions in odd-A tin isotopes

The reduced M2 transition probabilities $\text{11}\text{2}{}^{\mathrm{?}}{}_1\text{→}\text{7}\text{2}{}^{\mathrm{+}}{}_1$ in the odd-A isotopes ^109–121Sn are found to reveal a specific behaviour. B(M2) values are calculated in the framework of the quasiparticlephonon model. The coupling of a quasineutron with the 2⁺, 3^? and 2^? one-phonon core excitation is taken into account. Inclusion of all one-phonon 2^? states up to 24 MeV in the wave functions of the excited states $\text{11}\text{2}{}^{\mathrm{?}}{}_1\text{and}\text{7}\text{2}{}^{\mathrm{+}}{}_1$ reduces the theoretical B(M2) values by 3–4 times as compared to the single-particle values. The specific B(M2) dependence on the mass number appears to be due to the pairing effect.     

The quadrupole moments of the 5− states in 116Sn, 118Sn and 120Sn

The quadrupole interaction frequencies $\text{ω}{}_0\text{=}\text{3eQ}{}_1\text{V}{}_{\mathrm{zz}}\text{41(21-1)}\text{h}\text{?}$ in the 5^? state of ¹¹⁸Sn have been measured by time differential perturbed angular correlation technique in Sn, Sb and (95% Sn+5% Sb) environments. The ω₀ for ¹¹⁶Sn was determined in Sn environment only. With the help of the known electric field gradient ¹) of Sn in a Sn lattice the quadrupole moments have been deduced as $\text{Q(5}{}^{\mathrm{?}}\text{,}{}^{118}\text{Sn}\text{) = ±0.10(4) b}\text{and}\text{Q(5}{}^{\mathrm{?}}\text{,}{}^{116}\text{Sn}\text{) = ±0.165(60)}\text{b}$. These values together with the known²) quadrupole moment of the analogous 5^? state in ¹²⁰Sn are interpreted in terms of the pure single-particle model. The data exhibit the expected strong systematic variation of Q_I with the number of particles in the h_{$\text{11}\text{2}$}. subshell which is being filled with 1, 3 and 5 neutrons in ¹¹⁶Sn, ¹¹⁸Sn, and ¹²⁰Sn, respectively.     

Quadrupole moment of the 5−2, 134 keV state in 197Hg

The quadrupole interaction for the $\text{5}{}^{\mathrm{?}}\text{2}\text{, 134}\text{keV}$ state of ¹⁹⁷Hg in solid Hg was observed by the e^?-γ time differential perturbed angular correlation method. The quadrupole coupling constant ν_Q=126 (2) MHz is derived. By comparison with experimental quadrupole coupling constants for ¹⁹⁹Hg in Hg and HgCl₂ as well as for ²⁰¹Hg in HgCl₂ the quadrupole moment of the $\text{5}{}^{\mathrm{?}}\text{2}\text{, 134}\text{keV}$ state in ¹⁹⁷Hg is related to that of the ²⁰¹Hg ground state, which is known. The value $\text{Q(}{}^{197}\text{Hg}\text{,}\text{5}{}^{\mathrm{?}}\text{2}\text{, 134}\text{keV}\text{)=0.47(6)}\text{b}$ is deduced. This value is not in agreement with the assumption of a $\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ shell-model configuration for the 134 keV state. It is consistent with an interpretation of the $\text{5}{}^{\mathrm{?}}\text{2}$ level in terms of the core coupling model of de Shalit.     

Gamma decay of particle-core states in 209Pb

A γ-decay scheme for levels in ²⁰⁹Pb up to 4.13 MeV of excitation has been established by means of the reaction ²⁰⁸Pb(d, pγ)²⁰⁹Pb. In high efficiency p-γ coincidence measurements γ-cascades have been observed from the single-particle states and from core-excited states with very small single-particle strength. Assuming a qualitative validity of the weak-coupling model spins and main configurations of particle-core states can be deduced from their γ-decay. The $\text{J}{}^{\mathrm{\pi }}\text{= (}\text{3}\text{2}{}^{\mathrm{?}}\text{,}\text{5}\text{2}{}^{\mathrm{?}}\text{or}\text{7}\text{2}{}^{\mathrm{?}}\text{,}\text{11}\text{2}{}^{\mathrm{?}}\text{,}\text{15}\text{2}{}^{\mathrm{?}}\text{)}$ members of the $\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{?3}{}^{\mathrm{?}}$ multiplet could be located. A systematic manner of doublet splitting is found for the lowest states with main configuration $\text{(}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?1}}\text{?3}{}^{210}\text{Pb}\text{(0}{}^{\mathrm{+}}\text{, 2}{}^{\mathrm{+}}\text{, 4}{}^{\mathrm{+}}\text{, 6}{}^{\mathrm{+}}\text{, 8}{}^{\mathrm{+}}\text{)}$. A new decay branch of the $\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ single-particle state is attributed to an admixture of quadrupole core vibration.     

Molecular Rydberg transitions: Cyanogen chloride

The electronic absorption spectrum of cyanogen chloride has been investigated in the range 2200-1250 Å. The first s-Rydberg transitions, $\text{X}\text{?}{}^1\text{Σ}{}^{\mathrm{+}}\text{→}{}^3\text{Π}{}_1$ and $\text{X}\text{?}{}^1\text{Σ}{}^{\mathrm{+}}\text{→}{}^1\text{Π}{}_1$ have been assigned, and analyzed to yield exchange and spin-orbit coupling parameters. The relative intensities of these two transitions have been shown to accord with an intermediate coupling situation. The $\text{π → π}{}^1$ intravalence excitations, leading to ^1.3(Σ^?, Δ and Σ⁺) states, have been discussed. It has been shown that one or both of the ¹Σ^? and ¹Δ states have bent geometries and that the ¹Σ⁺ state is located (tentatively) at 79 755 cm^?1. Two $\text{σ → π}{}^1\text{π → σ}{}^1$ states have been assigned, one at 56 340 cm^?1, the other at 74 450 cm^?1. The latter assignment is tentative, being largely based on observed vibronic interferences between the $\text{X}\text{?}{}^1\text{Σ}{}^{\mathrm{+}}\text{→}{}^1\text{Π}{}_1$ transition and the 74 450 cm^?1 transition. A considerable amount of vibrational oscillator strength and quantum defect data is presented.     

A test of iso-scalar quadrupole renormalization in the 32− → 12−(Ex = 0.478 MeV) transition in 7Li

Electromagnetic studies have established that the $\text{3}\text{2}{}^{\mathrm{?}}\text{,}\text{1}\text{2}{}^{\mathrm{?}}$ ground state doublet in ⁷Li is well described by the LS coupling shell model, provided quadrupole effective charge is introduced. The results of microscopic calculations for the excitation of the $\text{1}\text{2}{}^{\mathrm{?}}$ level in inelastic proton scattering shown within indicate that an equivalent renormalization of the ⁷Li quadrupole neutron transition densities is also necessary. This verifies the assumption which was made in a previous calculation of the cross section for the excitation of the $\text{3}\text{2}{}^{\mathrm{?}}$ level in the ⁷Li+²⁴Mg reaction.     

Static quadrupole moment of the 8− state of 112In

The quadrupole coupling constant $\text{(}\text{eQV}{}_{\mathrm{zz}}\text{h}\text{)}$ of the 8^? 606 keV level of ¹¹²In has been measured by the DPAD method in the hexagonal lattice of metallic cadmium. The quadrupole moment of the level is deduced to be |Q| = 0.093(6) in agreement with the theoretical value for the configuration $\text{[π(}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?1}}\text{ν(}\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}\text{)}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}{}^{\mathrm{n}}\text{]}{}_{\mathrm{8?}}$.     

A study of the excited electronic states of 9-fluorenone

Some spectroscopic properties of the low-energy electronic states of 9-fluorenone have been examined. The spectra in paraffin matrices at 4.2°K show detailed vibrational spectra. Two fluorescence spectra are observed; a diffuse emission arises from 9-fluorenone crystals in the paraffin matrix, and a sharp emission is characteristic of the molecule. The sharp fluorescence is analyzed in terms of known a₁ vibrational fundamentals. The sharp absorption is a near mirror-image to the fluorescence, so Herzberg-Teller vibrations are not prominent. The polarization in the crystal spectrum allows this low-energy transition near 23 000 cm^?1 to be assigned ${}^1\text{B}{}_2\text{←}{}^1\text{A}{}_1$. Because there is no vibronic perturbation in fluorescence, and certainly no out-of-plane modes, a $\text{π}{}^1\text{← n}$ transition seen at about 26 000 cm^?1 is tentatively assigned ${}^1\text{B}{}_1\text{←}{}^1\text{A}{}_1$. Another sharp absorption system is seen at 31 000 cm^?1 in the paraffin matrices at 4.2°K (linewidth 6 cm^?1) but no fluorescence was detected. The polarized crystal spectrum indicated the assignment of this system and another very strong system at 40 000 cm^?1 to be ${}^1\text{B}{}_2\text{←}{}^1\text{A}{}_1$, while other systems at about 34 000 cm^?1 and 44 000 cm^?1 are ${}^1\text{A}{}_1\text{←}{}^1\text{A}{}_1$.The phosphorescence spectrum of pyrene-d₁₀ held in a single crystal of 9-fluorenone at 4.2°K has been recorded. No delayed fluorescence from the host crystal is observed at 4.2°K but is intense at 77°K. The energy difference between host and guest triplet levels is estimated to be about 900 cm^?1 allowing the lowest triplet state of 9-fluorenone to be placed at 17 800 cm^?1.     

Half-life of the h9/2 shell-model intruder-state isomer Au

The half-life of the $\text{9}\text{2}{}^{\mathrm{?}}$ shell-model intruder-state isomer in ¹⁸⁷Au has been measured by employing a technique in which each incoming event is tagged with a digital representation of time by means of a real-time clock. With this method we obtain a 2.3 ± 0.1 sec half-life for the $\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{→}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ E3 isomeric transition resulting in a retardation of 50 relative to the Weisskopf single-particle estimate.     

Neutron particle-hole electric dipole states in 206, 207, 208Pb

Inelastic proton scattering on ²⁰⁶Pb, ²⁰⁷Pb and ²⁰⁸Pb through isobaric analog resonances has been used to study neutron particle-hole excitations with large ground-state γ-branches in these Pb isotopes. Relative (p, p′) cross sections at 90° are extracted for structures selectively excited on the $\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{,}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{and d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{?}\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ resonances. Interpretation of excitations is ²⁰⁶Pb and ²⁰⁷ Pb in terms of coupling to states in ²⁰⁸Pb is discussed. Branching ratios for 1^?states in ²⁰⁸Pb at 4.84, 5.29, 5.94 and 6.31 MeV and the $\text{1}\text{2}{}^{\mathrm{+}}$ state in ²⁰⁷Pb at 4.63 MeV are deduced.     

Study of the photon spectrum in the decay KS0→π+π−γ

The branching ratio $\text{Λ(}\text{K}{}_{\mathrm{<mtext>S</mtext>}}{}^0\text{→π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{γ)}\text{Λ(}\text{K}{}_{\mathrm{<mtext>S</mtext>}}{}^0\text{→π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{)}$ has been determined to be (2.68±0.15)×10^?3 for photon energies $\text{E}{}_{\mathrm{\gamma }}{}^1$ greater than 50 MeV in the K_S⁰ rest frame. The decay K_S⁰→π⁺π^?γ is found to be dominated by the internal bremsstrahlung transition. The branching rato of a possible direct transition is found to be less than 0.06 × 10^?3 at 90% confidence level for $\text{E}{}_{\mathrm{\gamma }}{}^1\text{> 50}\text{MeV}$.     

Collective models of giant states with density-dependent interactions

Using a simple density-dependent interaction $\text{?αδ(r}{}_1\text{?r}{}_2\text{)+γρ}{}^{\mathrm{\sigma }}\text{(}\text{1}\text{2}\text{(r}{}_1\text{+r}{}_2\text{))δ(r}{}_1\text{?r}{}_2\text{)}$, with the parameters α and γ adjusted to give the correct binding energy and the correct radius, we show that the energy of the giant quadrupole state is √2. This is the same result obtained by Mottelson, Hamamoto and Suzuki, using, however, different methods. We then consider finite-range terms in the interaction, such as those considered by Vautherin and Brink, and obtain a fairly simple modification of the above result. In contrast to the above quadrupole result the energy of the giant monopole state is not unique but depends linearly on σ, the power of the density. The Inglis cranking model is used to get the relevant mass parameters. This model appears to work very well for high frequency vibrations.     

Resonance neutron capture gamma rays in 177Hf

Primary capture γ-rays have been studied for 38 ¹⁷⁷Hf neutron resonances with energies in the range 1–165 eV. Intensities were measured for 29 transitions ending at states with an excitation energy in ¹⁷⁸Hf up to 2050 keV. The analysis was facilitated by the previous knowledge of the spin and parity of all neutron resonances and of most low-lying states. For nine final levels, which had not previously been seen, information on J and π was deduced from the corresponding average intensities. The distribution of partial widths was fitted with a χ² function with ν = 1.38_?0.13^+0.18 degrees of freedom for E1 radiation and ν = 1.5_?0.40^+0.60 for M1 radiation. The average El reduced photon strength was found to be $\text{S}{}_{\mathrm{<mtext>El</mtext>}}\text{= 〈Γ}{}_{\mathrm{\gamma itij}}\text{/DE}{}_{\mathrm{\gamma }}{}^5\text{〉A}{}^{\mathrm{<mtext>?8</mtext><mtext>3</mtext>}}\text{= (4.8 ± 1.0) × 10}{}^{\mathrm{?15}}\text{MeV}{}^{\mathrm{?5}}$ and the ratio between El and Ml intensities equal to 5.5 ± 1.4. A comparison of this value for the El strength with those reported for other nuclei with A$\text{\$}\text{?}$= 100 showed that the intensities follow the A-dependence predicted by the Brink-Axel model. A non-statistical effect was observed, consisting of an enhancement of El transition probalilities to K = 2, 3 final states as compared to K = 0, 4 states.     

Measurement and interpretation of the 1-0 band of 14N16O at 1900 cm−1

The wavenumbers of the vibration rotation band lines of ¹⁴N¹⁶O are reported for the ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{-}{}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{-}{}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{-}{}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ subbands of the 1-0 transition in the infrared. The full set of spectroscopic constants for this band has been determined by direct approach using the analysis of Zare, Schmeltekopf, Harrop, and Albritton. In addition to the band origin ν₀ and the B, D, H constants for the lower and upper vibrational levels, the following spin-orbit coupling constants have been derived: $\text{A}\text{?}{}_0\text{= 123.02772 ± 0.00011}$ and $\text{A}\text{?}{}_1\text{= 122.78248 ± 0.00011}$ (in cm^?1). Apparent centrifugal corrections to these constants have been determined and the values obtained for them are $\text{A}\text{?}{}_{\mathrm{<mtext>D</mtext><mtext>0</mtext>}}\text{= (0.347573 ± 0.00051) × 10}{}^{\mathrm{?3}}$ and $\text{A}\text{?}{}_{\mathrm{<mtext>D</mtext><mtext>1</mtext>}}\text{= (0.337135 ± 0.00050) × 10}{}^{\mathrm{?3}}\text{cm}{}^{\mathrm{?1}}$. Λ-Type doubling constants evaluated by using both grating and tunable laser data are also reported.     

The ã3A2 ← X̃1A1 absorption spectrum of thioformaldehyde: A vibrational and rotational analysis

The results of a vibrational and rotational analysis of the banded $\text{a}\text{?}{}^3\text{A}{}_2\text{←}\text{X}\text{?}{}^1\text{A}{}_1$ transition in $\text{CH}{}_2\text{S}\text{CD}{}_2\text{S}$ are presented. Only three of the six vibrational modes are active in the spectrum with $\text{ν′}{}_2\text{=}\text{1320}\text{1012}$, $\text{ν′}{}_3\text{=}\text{859}\text{798}$, and $\text{2ν′}{}_4\text{=}\text{711}\text{516}\text{cm}{}^{\mathrm{?1}}$. The spin forbidden transition gains intensity primarily by a mixing of the ${}^1\text{A}{}_1\text{(π}{}^1\text{,π)}$ and ${}^3\text{A}{}_2\text{(π}{}^1\text{,n)}$ states. This is confirmed by a rotational analysis of the 0₀⁰ band of both isotopes. The rotational analysis shows that the coupling in the $\text{a}\text{?}{}^3\text{A}{}_2$ state is near Hund's case b and that the spin constants are nearly 10 times greater than those observed for CH₂O. A $\text{CNDO}\text{2}$ calculation shows that this difference is due to the greater spin orbit coupling of S in CH₂S and to the smaller energy differences between the $\text{B}\text{?}{}^1\text{A}{}_1\text{(π}{}^1\text{,π)}$, $\text{b}\text{?}{}^3\text{A}{}_1\text{(π}{}^1\text{,π)}$, $\text{X}\text{?}{}^1\text{A}{}_1$, and the $\text{a}\text{?}{}^3\text{A}{}_2\text{(π}{}^1\text{,n)}$ states. The r₀ structure calculated from the rotational constants is $\text{r}{}_{\mathrm{<mtext>CS</mtext>}}\text{= 1.683}\text{A}\text{?}$, $\text{r}{}_{\mathrm{<mtext>CH</mtext>}}\text{= 1.082}\text{A}\text{?}$, β_HCH = 119.6°, and α (out of plane) = 16.0°. A simultaneous fit of the vibrational levels in ν′₄ of CH₂S and CD₂S to a double minimum potential function yielded a barrier to molecular inversion of 13 cm^?1 and an equilibrium out-of-plane angle of 15°.     

Ultraviolet absorption spectra of Zn2 and Cd2 in solid argon and krypton at 10 K

Zinc and cadmium atoms have been condensed with argon and krypton at 10 K. The most intense absorption is due to the ${}^1\text{P}{}_1\text{←}{}^1\text{S}{}_0$ atomic transition, and a weak band is due to the ${}^3\text{P}{}_1\text{←}{}^1\text{S}{}_0$ atomic absorption. Structured absorptions at 252 and 254 nm in solid argon and krypton with vibrational spacings of 140-120 cm^?1 are due to the ${}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{←}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ transition of Zn₂. Similar 273 and 277 nm absorptions with 110-90 cm^?1 vibrational spacings are due to Cd₂ in solid argon and krypton, respectively.     

Magnetic moment of the 2− state in 92Nb

The g-factor of the $\text{[π(2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^1\text{v(2}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}{}^1\text{]}{}_2\text{?}$ state in⁹²Nb(τ = 6.2 μsec) was determined by means of perturbed angular distribution methods using the ⁹²Zr(p, n)⁹²Nb reaction in a liquid alloy. The extracted $\text{v(}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}$ magnetic moment is discussed in terms of the core-polarization effect.     

Band contour analysis of compounds with pure isotopes: The E fundamentals of HC35Cl3

The vibration-rotation transitions for v = 1 ← 0 of NO (${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$) have been studied by using the technique of laser magnetic resonance spectroscopy. Five magnetic resonance lines are observed with three CO laser lines in the range from 1859 to 1886 cm^?1. From these, three zero-field transition frequencies, v = 1 ← 0; $\text{R(}\text{3}\text{2}\text{)}$, $\text{P(}\text{7}\text{2}\text{)}$, and $\text{P(}\text{9}\text{2}\text{)}$ are obtained with an accuracy of ±0.0007 cm^?1. The molecular constants which have been determined by borrowing centrifugal constants from a previous infrared work are $\text{B}{}_{02}{}^1\text{= 1.72004 ± 0.00006}\text{cm}{}^{\mathrm{?1}}$, $\text{B}{}_{12}{}^1\text{= 1.70212 ± 0.00010}\text{cm}{}^{\mathrm{?1}}$, and $\text{G(v = 1) ? G(v = 0) (}\text{for}{}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{) = 1875.8470 ± 0.0007}\text{cm}{}^{\mathrm{?1}}$.