K-quantum Number Research Articles

12C + 12C resonances by a molecular model

Resonances observed in the 12C + 12C collisions are studied with a molecular model. At high spins J = 12–16, a stable dinuclear configuration is found to be an equator- equator touching one as is obtained in the 28Si + 28Si system. With K-quantum number being specified as rotation-vibration model, normal modes have been solved around the equilibrium, firstly. Furthermore, Coriolis coupling has been investigated by diagonalization among low- lying normal-mode states with K = 0 and K-excitation. It is found that the Coriolis coupling introduces about 30% of K-mixing into the K = 0 molecular ground states of J = 12–16. The analyses of the angular momentum coupling show up a dominance of the lowest L in the inelastic channel of the molecular ground state newly obtained. Thus alignments appear strongly in the inelastic channel, which is in agreement with the explanation by the band crossing model. Discussion is given on "why disalignments appear in the 28Si + 28Si system, in contrast to the above results".

Investigation of the symmetry properties and level density parameters of some superdeformed light even–even nuclei

In this study we have investigated the symmetry properties and R 4/2 energy ratio of energy bands for superdeformed light even–even nuclei from Z = 10 to 30 by the use of a simple and valid analytical relation obtained in terms of a K-quantum number, which is the projection of the total angular momentum on the axis of symmetry of a nucleus. Moreover, the nuclear level density parameters of the nuclei of interest have been calculated by considering different excitation bands of the observed nuclear spectra. The method used assumes equidistant spacing of the collective coupled state bands of the nuclei considered. The values of the calculated nuclear level density parameters and R 4/2 energy ratio have been compared with those of the experimental and compiled values and are in quite good agreement with the experimental and compiled results.

Is the K-quantum number conserved in the order-to-chaos transition region?

To study the order-to-chaos transition in nuclei we investigate the validity of the K-quantum number in the excited rapidly rotating 163Er nucleus, analyzing the variance and covariance of the spectrum fluctuations of γ-cascades feeding into low-K and high-K bands. The data are compared to simulated spectra obtained using a microscopic cranked shell model. K-selection rules are found to be obeyed for decay along excited unresolved rotational bands of internal excitation energy up to around 1.2 MeV and angular momenta 20ℏ⩽I⩽40ℏ. At higher internal energy, from about 1.2 to 2.5 MeV, the selection rules are found to be only partially valid.

Conservation of the K-quantum number in warm nuclei

The selection rules on the K-quantum number in rapidly rotating warm nuclei are investigated analyzing quasi-continuum spectra feeding into low-K and high-K bands in 163Er. The data are compared to simulated spectra obtained using the band mixing model predictions including the residual interaction and a term representing the effect of the K-quantum number on the rotational energy. K-selection rules are found to be obeyed by the decay along excited unresolved rotational bands of heat energy up to around 1.2 MeV and angular momentum 30 ℏ ⩽ I ⩽ 40 ℏ . In contrast, the results corresponding to higher heat energy of 1.2 to 2.5 MeV indicate that the selection rules are only partially satisfied.

Compound and rotational damping in warm deformed rare-earth nuclei.

The gamma decay in the quasicontinuum from selected configurations of the rotational nucleus 163Er has been measured with the EUROBALL array. A new analysis technique has allowed for the first time to directly measure the compound and rotational damping widths Gamma (micro) and Gamma (rot). Values of Gamma (micro) approximately 20 keV and Gamma (rot) approximately 200 keV are obtained in the spin region I approximately 30-40 variant Planck's over 2pi, in good agreement with microscopic cranked shell model calculations. A dependence of Gamma (micro) and Gamma (rot) on the K-quantum number of the nuclear states is also presented.

Violation and persistence of the K-quantum number in warm rotating nuclei

The validity of the K-quantum number in rapidly rotating warm nuclei is investigated as a function of thermal excitation energy U and angular momentum I, for the rare-earth nucleus 163Er. The quantal eigenstates are described with a shell model which combines a cranked Nilsson mean-field and a residual two-body interaction, together with a term which takes into account the angular momentum carried by the K-quantum number in an approximate way. K-mixing is produced by the interplay of the Coriolis interaction and the residual interaction; it is weak in the region of the discrete rotational bands ( U≲1 MeV), but it gradually increases until the limit of complete violation of the K-quantum number is approached around U∼2–2.5 MeV. The calculated matrix elements between bands having different K-quantum numbers decrease exponentially as a function of Δ K, in qualitative agreement with recent data.

Treatment of the K-quantum number in unimolecular reaction theory: insights from product correlations.

The connection between the K-quantum number and product correlations in the barrierless unimolecular dissociation of symmetric-top molecules is explored to establish a qualitative diagnostic for the treatment of the K-rotor dynamics in unimolecular reaction theory. We find that fragment scalar and vector correlations can provide guidance in this matter, and the photodissociation dynamics of thermal NCNO to form CN and NO at several dissociation wavelengths are presented to demonstrate the utility of this approach. The "goodness" of the K-quantum number can be related to the amount of energy in the conserved vibrational modes at the inner transition state. On the basis of measured correlated vibrational distributions, the K-quantum number is found to be approximately conserved at the inner transition state for the photodissociation of NCNO at 514, 520, and 526 nm. The methodology, involving a comparison of product distributions from the photodissociation of jet and thermal ensembles at identical wavelengths, is general and may be applied to previously studied systems that dissociate along barrierless potential energy surfaces, CF(3)NO and CH(2)CO. In addition, vector correlations serve as a means to probe the K-mixing at the outer transition state, and measured v-j correlations in the photodissociation of thermal NCNO are presented.

Probing the nature of the K-rotor in unimolecular reactions: Scalar and vector correlations in the photodissociation of NCNO

The photodissociation dynamics of thermal NCNO at 520 and 532 nm have been examined using transient frequency modulation Doppler spectroscopy to measure state-selected CN scalar and vector correlations. Previous work has suggested that the global vibrational and rotational distributions may be described using separate statistical ensembles/phase space theory (SSE/PST). We find that the correlated vibrational and rotational distributions are well described by SSE at 520 nm if the K-rotor is considered inactive. At both wavelengths studied, the correlation between the velocity and the rotational angular momentum vector of the CN product is found to be described by phase space theory with no restriction of the projection of the rotational angular momentum vectors along the relative velocity axis. This is indicative of approximate K-scrambling at the transition state, and a discussion of these results in light of the evolution of the K-quantum number is provided.

Vector and scalar correlations in statistical dissociation: The photodissociation of NCCN at 193 nm

Nascent Doppler profiles of CN (X 2Σ+) fragments from the 193 nm photodissociation of NCCN have been measured using high-resolution transient frequency modulated (FM) absorption spectroscopy. This new method is highly suited for Doppler spectroscopy of nascent photoproducts. The experimental line shapes suggest an asymptotic available energy of 5300±100 cm−1 and are well described by a model in which the available energy is partitioned between a statistical reservoir (4700 cm−1) and a modest exit barrier (600 cm−1). We have determined state dependent v⋅j correlations. A trend of j becoming increasingly perpendicular to v for the higher rotational states is in accord with phase space theory, although the observed correlations are more than twice as strong. The v⋅j correlations can be quantitatively modeled by further restricting the phase space model with an approximate conservation of the K-quantum number, the projection of total angular momentum about the linear axis of NCCN. Global rotational and vibrational product distributions have also been measured. The highest accessible rotational states are underpopulated, compared to a phase space calculation. The global vibrational distribution is substantially colder than the phase space theory predictions. Vibrational branching ratios for coincident fragments have been measured as a function of the detected CN state from a close analysis of high signal-to-noise Doppler profiles. The correlated vibrational distribution, P(v1,v2), shows an excess of vibrationless coincident fragments, at the expense of dissociation to give one ground state and one vibrationally excited CN fragment. The correlated formation of two vibrationally excited CN fragments is as likely as the phase space prediction, yet the formation of v=2 is strongly suppressed. The fragment vector and scalar correlations provide a highly detailed view of the loose transition state typical for reactions well described by statistical reaction theories.

Possible conservation of the K-quantum number in excited rotating nuclei.

The \ensuremath{\gamma} cascades feeding into low-K and high-K bands in ${}^{163}$Er are investigated analyzing variances and covariance of the spectrum fluctuations. From a large data set of 1${0}^{9}$ triple coincidences, \ensuremath{\gamma}-\ensuremath{\gamma} coincidence spectra gated by resolved low-lying rotational bands are analyzed. Low-K bands are found to be fed by a much larger effective number of cascades than high-K bands. The covariance between pairs of gated spectra shows that the cascades feeding low-K bands are different from those feeding the high-K bands. The persistence of the K-selection rules for the excited rotational bands within the angular momentum region $30\ensuremath{\Elzxh}\ensuremath{\le}I\ensuremath{\le}40\ensuremath{\Elzxh}$ is suggested as explanation.

State-to-state rotational energy-transfer measurements in the v2=1 state of ammonia by infrared–infrared double resonance

An infrared double-resonance laser spectroscopic technique is used to study state-resolved rotational (R–R, R–T) energy transfer in ammonia (14NH3) (self-collisions and between ammonia and foreign gases). NH3 molecules are prepared in selected rovibrational states of the v2=1 level using coincidences between CO2 -laser lines and ν2 fundamental transitions. Measurements of both the total rate of depopulation by collisions, and the rates of transfer into specific final rovibrational states (v,J,K) have been carried out using time-resolved tunable diode laser absorption spectroscopy. For NH3–NH3 collisions, measurements of total depopulation rates of selected JK states in v2=1 and ground-state recovery rates are found to be three and eight times larger, respectively, than the Lennard-Jones collision rate, in accord with theoretical expectations for polar molecules. A kinetic master-equation analysis of time-resolved level populations yields state-to-state rate constants and propensity rules for NH3–NH3 and NH3–Ar collisions. Individual rotational energy-transfer rates in v2=1 are slower than in the vibrational ground state, but still comparable to the Lennard-Jones collision frequency. Our experiments show that rotational energy transfer in v2=1 is not governed by simple ‘‘dipolelike’’ selection rules. They show fast rotational energy transfer, which can be related to long-range interaction potentials, but at the same time considerable amounts of ΔJ=2 and 3, ΔK=0, and ΔJ=1–4, ΔK=3, transitions, which may be attributed to higher-order terms in the multipole expansion of the intermolecular potential. No pronounced symmetry-state correlation and no preferred pathways were found except the preference for relaxation within a K stack and the expected separate relaxation of different nuclear-spin species, which can be labeled by their K-quantum number. Rates of collision-induced symmetry change (a↔s) in v2=1 are on the order of kas=4 μs−1 torr−1, smaller than kas in the ground state, but over an order of magnitude larger than that recently reported in the literature. Depopulation rates for other collision partners (Ar, H2, N2, and He) can be understood in terms of the intermolecular potentials. Comparisons are made between the relaxation rates measured in this work and infrared pressure-broadening coefficients reported in the literature.

A coexistence model for 18F

Three intrinsic four-particle-two-hole core-deformed states, labelled by the K-quantum number of the holes, are introduced to aid in describing the low-lying T = 0 even-parity levels in 18F. Since states of good angular momentum projected from only two of these three states can admix with the even- J two-particle states, the paucity of the even- J relative to the odd- J states can be explained in this fashion. The emphasis is on the reproduction of the empirical spectra using realistic potentials. However, calculations of the E2 transition probabilities and comparison of results with particle transfer data serve as tests of the model. A notable feature is that the T = 0 matrix elements between the 2p and 4p2h states are found to be considerably smaller than the T = 1 ones.

The dipole moment expansion for a tetrahedral molecule in the ground vibronic state

The expansion of the electric dipole moment operator in terms of angular momentum operators is examined in detail for a tetrahedral molecule in the ground vibronic state. The components of this centrifugal distortion moment in the molecule fixed frame are formally expanded to arbitrary order, with the expansion coefficients being given in terms of rotation matrices. For terms of rank j less than 15, general expressions are given for the matrix elements in the symmetric top basis of the space-fixed components of the dipole moment. The dependence of these matrix elements on the K-quantum number is shown to factor in such a way that previous first order calculations can be extended to second order by replacing the first order dipole coupling constant μ 2 (2) with a function of J which involves μ 2 (2) and two second order constants, μ 2 (4) and μ 4 (4) . Different functions are required for Q- and R-branch matrix elements and explicit expressions are given for both. The third order terms are examined in detail in the Appendix. A recurrence relation is derived for j < 15 between the tetrahedral harmonics of types A 2 and F 2. The implications of this work for distortion moment spectroscopy in tetrahedral molecules are discussed.

Two particle intrinsic excitations in 22Ne and 26Mg

A basis of two particle intrinsic states for 22Ne and 26Mg is defined in terms of the Hartree-Fock solutions for 20Ne and 24Mg. Mixing between the different intrinsic states is estimated from a deformed shell model. The model proceeds to describe the lowest 12 positive parity states in 22Ne and the lowest 15 in 26Mg. Spin, parity and K-quantum number assignments are proposed. These results are also compared with the existing shell model and projection model interpretations of 22Ne and 26Mg.