Coriolis Coupling Model Research Articles

Rotational spectroscopy of urea up to 500 GHz: The ground and eight excited vibrational states

Urea, ((NH2)2CO) is an important industrial and biological molecule. The new generation of the submillimeter telescopes, in particular ALMA, allows detection of extraterrestrial molecular spectra at unprecedented spatial and spectral resolutions. Some of the data presented here facilitated the recent definitive identification of urea in the interstellar medium (Belloche et al. Astron. & Astrophys. 628 (2019) A10:1-62). Its detection yields valuable insight into the mechanisms governing formation of complex prebiotic interstellar molecules. This paper reports spectroscopic analysis of the broadband rotational spectra of urea in the 210–500 GHz spectral range for the vibrational ground state and eight lowest excited vibrational states. The lowest excited vibrational state is only 61 cm−1 above the ground state and could be a useful temperature marker for astrophysical urea. The next two lowest pairs of excited states show significant interstate coupling, which has been successfully fitted with a Coriolis coupling model. Higher vibrational states also show evidence of significant coupling. Intensities of some rotational transitions of urea display nuclear spin statistical weights arising from the equivalence of the two ammonia groups, which enabled the assignment of symmetric and antisymmetric vibrational symmetry to the six lowest studied excited states. The vibrational energies of the new states have been determined from extensive relative intensity measurements and, together with vibrational symmetry, give insight into the highly anharmonic vibrational energy level structure.

Propionitrile in the two lowest excited vibrational states in the laboratory and on Titan

The rotational spectrum of propionitrile (ethyl cyanide, C2H5CN) in the two lowest excited vibrational states, v13=1 and v21=1, was studied in detail. The compiled experimental data set consisted of published line lists, lines measured from published spectra up to 645 GHz, and new measurements at frequencies from 8 to 331 GHz. The two states are subject to considerable mutual interaction but application of a- and b-axis Coriolis coupling model to the measured A-symmetry internal rotation substate transitions was found to be successful. A total of over 1900 transitions were fitted for J values up to 76 and Ka up to 24, resulting in determined vibrational separation between the two states ΔE=6.2070246(14) cm−1, and Coriolis coefficients |ζ13,21a| = 0.378, |ζ13,21b| = 0.127, in good agreement with quantum chemistry calculations. The new line catalog was used to model ALMA spectra of Titan’s atmosphere from 2016, fitting many weak lines not previously modeled. By including the vibrationally excited lines of C2H5CN and a new partition function, we derive a disk-averaged volume mixing ratio estimate in 2016 of 7.8 ± 0.2 ppb assumed constant above 300 km.

THE EXPRESSIONS FOR THE SUPER-ALLOWED BETA-DECAY RATES IN THE CORIOLIS COUPLING MODEL: APPLICATION TO THE 1d5/2 SHELL NUCLEI

The expressions for super-allowed beta-decay transition rates have been derived within the context of the Coriolis coupling model. The derived expressions, valid for the beta-decay between any two mirror nuclei, have been applied to calculate super-allowed beta-decay transition rates of 21 Na , 23 Mg , 25 Al , and 27 Si . Without the use of any hindrance factor, the calculated rates agree well with the data and also with the calculations done using the shell model with configuration admixture.

Infrared diode laser spectroscopy of the Ne–D2O van der Waals complex: Strong Coriolis and angular-radial coupling

Four internal-rotation/vibration bands of the Ne-D(2)O complex have been measured in the v(2) bend region of D(2)O using a tunable infrared diode laser spectrometer to probe a slit supersonic expansion. Three ortho bands are excited from the ground state Σ(0(00)) to the Σ and Π(1(11), υ(2) = 1) internal rotor states and the n = 1, Σ(0(00), υ(2) = 1) stretching-internal rotor combination state. Strong perturbations between the excited vibrational states are evident. The observed spectra are analyzed separately with a three-state J-dependent Coriolis plus J-independent angular-radial coupling model [M. J. Weida and D. J. Nesbitt, J. Chem. Phys. 106, 3078 (1997)] and a three-state Coriolis coupling model [R. C. Cohen and R. J. Saykally, J. Chem. Phys. 95, 7891 (1991)]. The former model works more successfully than the latter. Molecular constants for the ground and excited vibrational states of ortho (20)Ne-D(2)O isotopomer as well as the Coriolis and angular-radial coupling constants are determined accurately. The van der Waals stretching frequency is estimated to be ν(s) = 24.85 cm(-1) in the ground state and decreases to about 20.8 cm(-1) upon vibrational excitation of the D(2)O bend.

High resolution mid-infrared spectroscopy of ArH2O: The v2 bend region of H2O

Six internal rotation/vibration bands of ArH2O are observed in a slit supersonic expansion via direct absorption of a tunable diode laser in the v2 bend region of H2O. The spectra obtained for the ortho H2O manifold are well represented by a pseudodiatomic model with nearly free internal rotation of the H2O subunit. By way of contrast, the para bands show significant mixing between the internal rotor and stretch states, indicative of strong angular-radial coupling in the intermolecular potential. The spectra for the para Ar–H2O species can be deperturbed based on a three state Coriolis plus angular-radial coupling model which includes microwave, far-ir and near-ir data. The results indicate a redshift of ≈0.58 cm−1 upon bend excitation of the H2O subunit, and in general rather modest changes in the excited state intermolecular potential from the ground state potential. No indication of predissociation broadening is found, and the instrument-limited linewidths place a lower limit on the vibrational lifetime in the excited state of τ⩾7.2(6) ns.

Level spectra, electromagnetic moments and transition rates and spectroscopic factors for odd rhodium isotopes in the coriolis coupling model

Properties of low-lying positive- and negative-parity states of 97,99,101,103,105,107,109Rh at low excitation energies have been analyzed in terms of a Coriolis coupling model. The model can account for the general trend of the level schemes for states of both parties. In particular, the 9 2 , 7 2 , and 5 2 triplet near the ground state, the occurrence of multiple 13 2 and at least one 15 2 and 19 2 state of positive parity are reasonably reproduced by the model. Similarly, 1 2 ground-state spin followed by a ( 3 2 , 5 2 ) doublet, and one or more 13 2 and 17 2 states of negative parity are adequately understood in terms of the model. The calculated electromagnetic dipole and quadrupole moments and magnetic dipole and electric quadrupole transition rates are in broad agreement with the observed ones. This is achieved without the use of any effective charge. The general trend of observed spectroscopic factors for pick-up reactions is in agreement with the calculated ones. The results are presented as a function of deformation. Because of the sparsity of data on many of these isotopes, no attempt has been made to find the best fit for each isotope individually. Since the model can reasonably reproduce the general trend of level schemes, electromagnetic properties and spectroscopic factors, one may conclude that the Coriolis coupling model provides a good description of the nuclear properties of these isotopes.

High spin states of 83Sr

The reactions 80Kr(α, n) 83Sr and 82Kr(α, 3n) 83Sr were used to populate excited states of high spin in 83Sr. The de-excitation of these states was studied by in-beam γ-ray spectroscopy. A number of new high-spin states have been observed. The results are discussed within the framework of the Coriolis-coupling model and the cluster-core coupling model.

A study of the76Se(3He,d)77Br and78Se(3He,d)79Br reactions

The 76Se(3He,d)77Br and 78Se(3He,d)79Br reactions have been studied at a bombarding energy of 41 MeV with a magnetic spectrograph. In 77Br, 23 levels were resolved, and in 79Br, 26 levels were resolved. The l-transfer values and spectroscopic strengths for most of these levels were determined from DWBA analyses. The results are compared with the predictions of the Coriolis coupling model with pairing residual interaction of Scholz and Malik.

Study of the 77, 79, 81, 83Se level structure with the [formula omitted] reaction

Differential cross-section and vector-analyzing-power data were obtained for an incident deuteron energy of 12.5 MeV for the 76,78,80,82Se(d, p) 77,79,81,83Se reactions. The results are compared with the predictions of the DWBA theory to determine l-values, spins, parities and spectroscopic factors of the resolved states. Magnetic spectrograph measurements were made to determine the excitation energies of the states studied as well as for a number of additional levels in each isotope. A precise determination of the 82Se(d, p) 83Se Q-value was also made, yielding a value of 3.5934±0.0030 MeV. Spin and parity assignments have been made to 16 states in 77Se, 22 states in 79Se, 17 states in 81Se, and 15 states in 83Se. In addition, tentative spin assignments were made to one state in 79Se and to three states in 83Se. A sum-rule analysis was carried out and comparisons made to previous work and to the predictions of the simple pairing theory. The results are in general agreement with the Coriolis-coupling model calculations of Heller and Friedman.

Investigation of the level schemes of 73,75,77As via the ( 3He, d) reaction

The reactions 72, 74, 76Ge( 3He, d) were investigated at E lab = 23 MeV with a multigap and a Q3D magnetic spectrograph. Some 30 new levels up to E ∗ ≈ 4 MeV have been found. The level schemes of the odd As isotopes 73, 75, 77As up to E ∗ ≈ 4 MeV seem to be rather independent of the neutron number. The good agreement of the low-lying level structure with the Coriolis-coupling model including a pairing force was verified and the vacancies of low-lying shell model states were extracted and compared with the simple pairing theory.

Theoretical predictions of electromagnetic properties of1g92odd-neutron nuclei in the Coriolis coupling model

Magnetic dipole and electric quadrupole moments and reduced transition rates of several 1g$sub 9$/$sub 2$ nuclei are calculated using the wave functions generated in a previous paper. The pattern of wave functions is shown to support the application of a fixed parameter Coriolis coupling model to nuclei in this region. By a total inclusion of both diagonal and nondiagonal single-particle contributions, theoretical magnetic moments for ground and first excited states of both parities are brought into exceptional agreement with experiment. In particular, this analysis resolves the essential equality of $mu$ (7/2) and $mu$ (9/2) in $sup 83$Kr as opposed to the expected equivalence of their g factors. Quadrupole moments, calculated without resorting to effective charges, are generally well predicted. Theoretical transition rates are calculated in two instances and agree with experiment.

Coriolis-coupling model applied to odd-neutron nuclear spectra of the1g92shell

A Coriolis-coupling model extended to include a residual pairing type interaction is applied to investigate the energy levels of low lying states of the odd nuclei of the $1{g}_{\frac{9}{2}}$ shell $73<A<87$. This deformed rotational treatment includes spectra of both parities originating from overlapping states of the $N=4$ and $N=3$ positive and negative parity shells. Single particle energy levels and wave functions throughout a shell are computed using spin-orbit and well-flattening parameters $C=\ensuremath{-}0.26\ensuremath{\hbar}{\ensuremath{\omega}}_{0}$ and ${D}_{N=4,3}=\ensuremath{-}0.040\ensuremath{\hbar}{\ensuremath{\omega}}_{0}$ $\ensuremath{-}0.053\ensuremath{\hbar}{\ensuremath{\omega}}_{0}$, respectively, the latter values being consistent with ${d}_{\frac{5}{2}}$ parentage states of $^{79}\mathrm{Se}$ (positive parity) and ${f}_{\frac{5}{2}}$ states of $^{83}\mathrm{Kr}$ (negative parity). Inclusion of an extracore pairing interaction primarily introduces a multiplicative effective overlap which serves as a quenching factor to the strength of off-diagonal Coriolis coupling terms. All parameters in the analysis are taken from available experimental considerations. The rotational constant $A$ and deformation $\ensuremath{\beta}$, in particular, are derived from the location of the first excited ${2}^{+}$ state of the neighboring even-even nucleus and its observed $E2$ transition rate to the ground state. For each set of parameters both a single particle and a Coriolis coupling diagonalization are performed over an entire shell of 10 or 15 Nilsson states to obtain final negative or positive parity spectra and wave functions. The results of this essentially fixed parameter model are presented and compared with experimental determinations with which they are in substantial agreement. In general, the model favors a prolate description for the nuclei in this region. Energy excitation spectra are all in general agreement, and in particular: (a) ground state spins and lowest lying opposite parity spins are always correctly predicted; (b) many otherwise anomalous low lying and often ground state ${7/2}^{+}$, ${5/2}^{+}$ spins are well predicted. The systematic reproduction of experimental spectra provided by the model points to the validity of a statically deformed interpretation of the odd neutron nuclei of the $1{g}_{\frac{9}{2}}$ shell, in contrast to the purely spherical and vibrational approaches to which the region has been restricted in the past.NUCLEAR STRUCTURE $^{73}\mathrm{Ge}$, $^{75,77,79,81}\mathrm{Se}$, $^{83,85}\mathrm{Kr}$, $^{87}\mathrm{Sr}$; calculated levels, $I$ $\ensuremath{\pi}$. Deformed Coriolis coupling treatment with pairing. Both parties.

Study of 47Ti with the 45Sc( 3He, p) 47Ti and 45Sc( 3He, pγ) 47Ti reactions

The 45Sc( 3He, p) 47Ti reaction has been studied at E( 3 He) = 17 MeV by magnetic analysis with the Argonne split-pole spectrograph. The energy resolution was about 25 keV (FWHM). The excitation energies of 22 levels at excitations up to 7.5 MeV were determined, and the angular distributions associated with them were measured and analyzed in terms of two-nucleon transfer DWBA calculations. Angular distributions indicating orbital angular-momentum transfer L np = 0 were observed for two states: the analog state at 7.346 MeV and the 3.223 MeV state which is assumed to be the antianalog. The decay of the 47Ti levels was studied by measuring the p-γ coincidences in the 45Sc( 3He,pγ) reaction at E( 3 He) = 12 and 17 MeV, and level and decay schemes were established on the basis of the results. In the discussion of the properties of the 47Ti states, the results of the present work are compared with those obtained in one-nucleon transfer reactions, and all the data are compared with the results of calculations based on two different models for 47Ti. Comparing the reaction data with theory allows us to single out eleven 47Ti states that have simple configurations and are reasonably well described by theory. However, in examining the γ-decay data to obtain a more stringent test of the current models, we found the models incapable of accounting for the γ-decay of some of these simple states. In particular, the 1.548 MeV state, which seemed to have a large (f 7 2 ) 6( P 3 2 ) component, is not well described by the Coriolis-coupling model.

Gamma decay of the low-energy levels of49V

The49V level scheme has been studied by the49Ti(p, nγ)49V reaction at various bombarding energies between 2 and 4 MeV. Gammaray single and coincident spectra have been observed; the branching ratios of various levels were measured and information about their spin and parity has been deduced. The level scheme is in good agreement with the results of the Coriolis coupling model calculations of Malik and Scholz. Some even-parity levels are present which show the typical pattern of a rotational band based upon the 1d3/2 hole excitation.

Hyperfine structure investigations of 51Mn and 52mMn

Abstract The atomic-beam magnetic resonance method has been used to study the hyperfine structure interaction in 51Mn(45 min) and 52mMn(21 min). The results are for 51Mn: I = 5 2 , |a| = 74.835(1) MHz, |b| = 0.024(4) MHz ( b a > 0) , |μI| = 3.56(1) n.m., |Q| = 0.50(10) b, and for 52mMn: I = 2, |a| = 0.200(2) MHz, |μI| = 0.0076 n.m.. The nuclear moments have been calculated from the measured h.f.s. coupling constants using the known values of a, b, μI and Q for 55Mn. The results are compared with shell-model and Coriolis coupling model calculations.

Structure of 51Cr via 48Ti( 4He, nγ) and 51V(p, nγ) prompt γ-ray spectrometry

The level structure of 51Cr has been studied in some detail via prompt γ-ray energy and intensity measurements utilizing a NaI(Tl)-Ge(Li) anti-Compton spectrometer and a 511-γ-511 escape peak spectrometer via the 51V(p, nγ) reaction with proton energies in the range 2.6–6.0 MeV and via the 48Ti( 4He, nγ) reaction with t4He ++ energies in the range 12.0–15.0 MeV. Many of the γ-rays associated with levels in 51Cr were identified with the ( 4He, nγ) or the (p, nγ) reaction by means of nγ coincidence measurements employing an organic phosphor as the fast neutron detector and a Ge(Li) γ-ray detector. Characterization of many levels populated in the (p, nγ) reaction was achieved by means of thresholds for individual γ-rays obtained from measurement of excitation functions of individual γ-rays and from the γγ coincidence relationships established in on-beam γγ coincidence measurements in the 51V(p, nγ) reaction at E p = 5.0 MeV employing a NaI(Tl) and a Ge(Li) detector. It was thus established that 39 levels in 51Cr are populated in these reactions. The levels at 2255.7, 2385.6, 2767.1 and 3001.6 or 3004.1 keV which were observed in these experiments have not been reported previously. The rest of the levels studied in this work have been studied previously by means of (d, p), (p, d) and ( n th , γ) reactions. With the exception of the first six levels, the levels reported here have not been reported previously in the (p, nγ) or the ( 4He, nγ) reactions. For the levels below 2704 keV in 51Cr branching ratios for deexcitation of these levels by γ-decay were obtained by averaging the measured angular correlation of each γ-ray about the beam direction. The new γ-ray information from the present study was used in conjunction with the results of previously reported (d, p) reaction studies to make definite J π assignments to many stripping levels in 51Cr and to place limits to the J π values for many levels which were reported earlier to exhibit proton angular distribution patterns from the (d, p) reaction non-characteristic of a stripping reaction. In this work a number of γ-rays were assigned to deexcite levels in 51V that are populated via the 51V(p, p'γ) and 48Ti( 4He, pγ) reactions and which were found to compete to a small extent with the (p, nγ) and (4He, nγ) reactions. A tentative decay scheme for the deexcitation of levels in 51V is offered. The level structure of 51Cr and of 51V is compared with previously reported results of the Coriolis coupling model for the f 7 2 . shell and good qualitative agreement in the level ordering is found.

Measurement and interpretation of electromagnetic transitions in 51V

Angular correlation measurements in the 180° geometry for the 48Ti(α, pγ) 51V reaction were used to determine the γ-ray decay properties of states in 51V at 0.32, 0.93, 1.61, 1.81, 2.41, 2.55, 2.68 and 2.70 MeV. Coulomb excitation measurements with 32S ions, using a thick 51V target and a Ge(Li) detector, were used to deduce the B(M1) and B( E2) reduced transition probabilities for the decays of the 0.32, 0.93, 1.61 and 1.81 MeV states. For these states the M1 transitions are found to be retarded by factors ranging from about 400 to over 10000, while the E2 transitions are enhanced by about an order of magnitude relative to the Weisskopf estimate. Shell-model calculations were performed for 51V considering all basic three proton states in the f-p shell and assuming a 48Ca core. Kuo and Brown two-body matrix elements were used. Remarkably good agreement is obtained between the calculated and measured transition rates, supporting the shell-model predictions of a high-configuration purity for the six levels of the basic f 7 2 3 multiplet. By contrast, the B(M1) values predicted by the strong Coriolis coupling model of Scholz and Malik strongly disagree with the measured values, generally being two or three orders of magnitude too large. We conclude that the spherical shell model provides an excellent description of the low-lying states in 51V and, contrary to Scholz and Malik, we find no evidence for deformation in this nucleus.

Structure of 21Na from the 24Mg(p, α) 21Na reaction

The lower excited states of 21Na were studied using the 24Mg(p, α) 21Na reaction at a bombarding energy of E p = 17.5 MeV. From analysis of particle-ray-γ angular correlations the spins of the 332, 1723 and 2834 keV states were found to be J = 5 2 or ( 3 2 ), 7 2 or ( 3 2 ) and 9 2 or ( 5 2 ) , respectively. Branching and multipole mixing ratios were obtained as well as evidence for a doublet of states with excitation energies 2833.8 ± 4.0 and 2803.5 ± 5.0 keV. This removes a puzzle of long standing concerning an apparent missing state in 21Na as compared to the mirror nucleus 21Ne. The experimental information obtained in the present study is compared with that for the mirror nucleus, 21Ne, and discussed in terms of a Coriolis coupling model. These data, and those to be reported in subsequent papers for adjacent nuclei, suggest strongly that these nuclei may well be among the most rigid in nature.

Use of the (γ,γ′) Reaction for Studying the Energy Levels ofAs75

Elastic and inelastic nuclear resonant scattering of monochromatic photons from $^{75}\mathrm{As}$ have been studied using a 47-cc Ge (Li) detector. The $\ensuremath{\gamma}$ source was provided by thermal-neutron capture in iron. The energy of the resonance level in $^{75}\mathrm{As}$ was found to be 7.646 MeV. Assuming the high-energy lines to be primary transitions deexciting the resonance level, 25 energy levels were found from the ground state up to 2.6 MeV, seven of which may be identified with recently reported levels. By measuring the angular distribution of the scattered radiation, the spin of the scattering level was determined to be \textonehalf{} and the spins of 14 low-lying levels were thus found to be either \textonehalf{} or $\frac{3}{2}$. The total radiative width of the resonance level was determined and was found to be $\ensuremath{\Gamma}=0.36\ifmmode\pm\else\textpm\fi{}0.10$ eV and $\frac{{\ensuremath{\Gamma}}_{0}}{\ensuremath{\Gamma}}=0.11$. The $^{75}\mathrm{As}$ levels are compared with the predictions of the Coriolis coupling model.

Proton transfer on 50V via the ( 3He, d) reaction

The 50V( 3He, d) 51Cr reaction has been investigated at an incident energy of 7.5 MeV. Angular distributions were measured in the MIT multiple-gap spectrograph and analysed in the distorted-wave Born approximation. The Q-value for the ground state transition was measured to be 4.031±0.015 MeV. Transitions to 44 excited states were observed below 6.0 MeV of excitation. The low-lying part of the 51Cr level scheme is discussed in terms of the shell model and the Coriolis coupling model.