Deuteron Quadrupole Research Articles

Deuteron Magnetic Resonance Study of Some Crystals Containing an O—D···O Bond

A deuteron magnetic resonance study was made on four compounds with an O—D···O hydrogen bond of different strengths. The deuteron quadrupole coupling constant eqQ, asymmetry parameter η, and the directions of the field gradient tensor were determined. The eqQ and η obtained are: KDCO3154.4±0.6 kc/sec,0.194±0.018,(COOD)22D2OD1(water)230.3±2.0 kc/sec,0.062±0.006,D2(water)219.1±2.0 kc/sec,0.16±0.03,} (at−70∘C) D1 and D2121±3 kc/sec,0.93±0.02,(at 67∘C) D3(carboxyl)139.2±0.8 kc/sec,0.098±0.005,ND4D2PO4 (acid D)119.6±0.8 kc/sec,0.053±0.008,K, D−maleate 56.0±0.8 kc/sec,0.53±0.07. The results are discussed in relation to the crystal structure in each case. It was found that the oxalic acid dihydrate crystal used was a new modification, different from the ordinary one. Reorientational motion of a water molecule similar to that in other hydrated crystals was observed in oxalic acid dihydrate from the measurement at different temperatures. A barrier to this motion of 10.0 kcal/mole was determined from the temperature dependence of the linewidth. In each compound studied, correlation between the principal axis directions of the field-gradient tensor and the local atomic arrangement in the crystal can be readily observed. The direction of the largest principal component of the field gradient tensor is in good agreement with the O—D direction or the O—D···O direction. The direction of the second principal component is generally in good agreement with the normal to the plane defined by[Complex chemical formula]The deviation from the latter rule can be seen in D1 of oxalic acid dihydrate where O—D···O differs greatly from a straight bond. A marked decrease of eqQ with increasing hydrogen-bond strength is observed. Both the field gradient and the square of the OH stretching frequency as a function of O···O distance are in fairly good agreement with each other, similar to the near equality of the field gradient and force constant in diatomic hydrides. The change in the electronic contribution to the field gradient with O–H distance in the hydrogen bonded system is estimated.

Hyperfine Structure in the Microwave Spectrum of HDO, HDS, CH2O, and CHDO : Beam-Maser Spectroscopy on Asymmetric-Top Molecules

Hyperfine structure in the 220→221 rotational transition of HDO at 10 278.2 Mc/sec and HDS at 11 283.8 Mc/sec, and in the 211→212 rotational transition of CH2O at 14 488.6 Mc/sec and CHDO at 16 038.1 Mc/sec, has been investigated with a high-resolution beam maser microwave spectrometer. Linewidths of 5 kc/sec have been obtained. The hyperfine Hamiltonian for an arbitrary number of nuclei with quadrupole, spin—rotation, and spin—spin interactions is discussed, and the matrix elements of the Hamiltonian and the intensities of hyperfine transitions calculated in terms of the tabulated 6j coefficients. Quadrupole and spin—rotation constants and bond lengths which have been determined are, for the 220 state of HDO: (eqJQ)D = 79.3±0.3 kc/sec, CH = —43.47±0.11 kc/sec, CD = —2.33±0.02 kc/sec; for the 221 state of HDO: (eqJQ)D = 79.6±0.3 kc/sec, CH = —43.63±0.13 kc/sec, CD = —2.20±0.02 kc/sec; for the 220 state of HDS: (eqJQ)D = 42.9±0.4 kc/sec, CH = —25.03±0.13 kc/sec, CD = —0.47±0.02 kc/sec; for the 221 state of HDS: (eqJQ)D = 43.3±0.4 kc/sec, CH = —25.45±0.13 kc/sec, CD = —0.22±0.02 kc/sec; for CH2O: CH (211) — CH (212) = 2.26±0.13 kc/sec, CH (211) = 0.65±0.50 kc/sec, 〈1/rHH3〉—⅓ = 1.898±0.017 Å; for CHDO: (eVξξQ)D = 170.0±2.0 kc/sec (where Vξξ is the second derivative of the electrostatic potential along the CD bond), CH (211) — CH (212) = 2.42±0.50 kc/sec, CD (211) — CD (212) = 0.25±0.10 kc/sec, CH (211) = 0.2±1.0 kc/sec, CD (211) = 0.13±0.20 kc/sec, and 〈1/rHD3〉—⅓ = 1.88±0.10 Å. The Vξξ calculated from the deuteron quadrupole coupling constants are, for HDO: 1.56×1015 statvolt/cm2; for HDS: 0.76×1015 statvolt/cm2; and for CHDO: 0.83×1015 statvolt/cm2.

Deuteron Quadrupole Coupling in Diatomic ``Hydrides''

For LiD and DF, the deuteron quadrupole coupling constant (eqQ/h) has been calculated with single-determinant SCF-LCAO-MO functions. The results obtained are 38 kc/sec for LiD and 373 kc/sec for DF, in rather satisfactory agreement with the recently measured values (30±3 kc/sec for LiD and 340±40 kc/sec for DF). To evaluate the molecular integrals required for the determination of q, a formulation in terms of confocal elliptic coordinates was used. This made possible the introduction of certain auxiliary functions that are very convenient for the calculation of field gradient and related integrals. A comparison of the quadrupole coupling constants obtained with a number of different molecular orbital functions is presented. The results demonstrate the importance of using atomic basis functions with exponents optimized for the molecular system and suggest that exact Hartree-Fock functions may yield relatively reliable values for field gradients and other one-electron weak-interaction parameters. A calculation of the field gradient at the Li nucleus (q = —0.0401 a.u.) yields a value of —3.7×10—26 cm2 for the Li7 quadrupole moment when combined with the coupling constant measurement of +346±1 kc/sec.

Role of spin-orbit force in nuclear interactions

The two-body problem (scattering and bound state) has been solved exactly by considering an extension of Yamaguchi's non-local separable potential so as to include a two-body spin-orbit force. The parameters of the potential have been determined by obtaining their exact relationships with the low-energy experimental data (scattering length, effective range, deuteron binding energy, quadrupole and magnetic moments and the D-state probability). It is found that in order to fit the data, particularly the magnetic moment, the strength of the spin-orbit force must be comparable to that of the tensor force. This potential has been applied to the evaluation of the spin-orbit energy splitting in the nuclei Ca 41 and O 17. It is found that the tensor force by itself gives the wrong sign of the splitting and that it is overcompensated by a large contribution (of the correct sign) arising from the two-body spin-orbit force.

Ground-State Inversion Spectrum of N14D3

The inversion spectrum of N14D3 has been investigated between 1500 and 1620 mc/sec. A revised formula for the rotational fine structure was obtained to fit 17 observed lines. Splitting of K = 3 lines into two components was found in good agreement with predicted values. Nitrogen satellites were observed and the values (eQq)N = 4080–3 kc/sec and α = 2±2 kc/sec were assigned to the nitrogen quadrupole and magnetic coupling constants, respectively. Hyperfine structure due to removal of the K degeneracy was observed in K = 1 lines. Applying the theory of Hadley, calculated and observed line contours were brought into agreement. Assuming cylindrical symmetry about bonds, the value (eQq)D = 200±20 kc/sec was obtained for the deuteron quadrupole coupling constant. A value ε = 1.9±0.5 kc/sec was obtained for the magnetic coupling constant between deuteron spins and molecular rotation.

Charge Density in the Deuteron

The phenomenological theory of the deuteron charge distribution is discussed. Finite nucleon sizes are included. The theory is applied to the deuteron quadrupole moment, the low-energy photonuclear reaction $\ensuremath{\gamma}+d\ensuremath{\rightarrow}n+p$, and elastic electron-deuteron scattering. It is shown that these phenomena can be given a consistent phenomenological treatment under the simplest assumptions.

Theoretical Study of the Hyperfine Structure in the Inversion Spectra of the Deutero-Ammonias

The energy splittings in the inversion spectra of N14D3, N14HD2, and N14DH2 caused by nitrogen and deuteron quadrupole interactions with the molecular electric field, the interactions of the nuclear spins with the molecular magnetic field, and the spin-spin interactions are found. The molecular coupling scheme of Van Vleck is used to treat the Hamiltonian to second order in the electronic energies. Group theory is used to select wave functions which simplify the solution of the secular equations. For N14D3 thirteen constants appear in the energy expressions. Order of magnitude estimates for eleven of these constants can be made using data from the experimental work on N14H3. No estimate is made of the deuteron quadrupole coupling constants. With N14HD2 and N14DH2 twenty-four constants appear in each case. Order of magnitude estimates can be made for only nine of these.

Electromagnetic Effects in Two-Nucleon Systems

Corrections to the electromagnetic properties of two-nucleon systems are examined by means of the relativistic two-body equation. An effective addition to the potential is derived, which describes the properties of the system in an external electromagnetic field. In particular, the correction to the deuteron's quadrupole moment is evaluated to lowest order in the meson-nucleon coupling. The result, for pseudoscalar (pseudoscalar) symmetric theory, is $\ensuremath{\Delta}Q=\ensuremath{-}1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}28}(\frac{{g}^{2}}{4\ensuremath{\pi}})$ ${\mathrm{cm}}^{2}$.

The Effect of the Tensor Force on the Binding Energy of the Alpha-Particle

The binding energy of the 4He nucleus is calculated by the variation method, assuming charge-independent neutral two-body forces, using Yukawa wells, not necessarily of the same range, for the central and tensor parts of the interaction. The wave function chosen represents a mixture of the principal 1S0 and the principal 5D0 states, the radial wave functions being of a simple exponential type. With the nuclear parameters adjusted to fit the deuteron energy and quadrupole moment, and other low-energy data, it is found that the introduction of the tensor force greatly reduces the large value of the 4He energy, obtained in the purely central force case. Whereas equal ranges yield a very small binding, the unequal ranges, which according to Pease and Feshbach fit the triton, give reasonable values for 4He. Thus it seems possible that a phenomenological two-body interaction of the above type may give consistent results in the two-, three-, and four-body problems. For the triton the same type of wave function gives rather poor results, compared with another exponential function, used previously.

Vibrational and Centrifugal Effects on Nuclear Interactions and Rotational Moments in Molecules

The effects of zero point vibration and centrifugal stretching of molecules upon the spin-spin magnetic interaction, the spin-rotational magnetic interaction, the molecular rotational magnetic moment, the magnetic shielding of the nucleus, and the molecular diamagnetic susceptibility of the molecule are discussed. Expressions for these quantities with vibrational and centrifugal effects included are given in detail for diatomic molecules and numerical calculations for the cases of ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$. It is shown that from measurements of the rotational magnetic moments of both ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ or of ${\mathrm{H}}_{2}$ in two different rotational states, one can calculate the variation with internuclear separation of the high frequency terms of the molecular diamagnetic susceptibility. Measurements on the spin-rotational magnetic interactions in both ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ provide information on the variation of this interaction with internuclear spacing and thereby supply important corrections that are needed in calculating the nuclear magnetic shielding from the spin rotational magnetic interaction and in measuring the ratio of the proton magnetic moment to that of the deuteron. These calculations also supply a correction to the spin-spin magnetic interaction that must be used in determining the deuteron quadrupole moment from experiments with ${\mathrm{D}}_{2}$.

On The Two-MesonTheory1

Main consequences of the two-meson theory by Marshak and Bethe on the one hand and that by Sakata are compared with experiments concerning $\ensuremath{\pi}$- and $\ensuremath{\mu}$-mesons. It is shown that the pair type interaction between $\ensuremath{\pi}$-mesons and nucleons in M. B. theory contradicts with frequent occurrence of stars produced by $\ensuremath{\pi}$-mesons, whereas the assumption in Sakata theory that $\ensuremath{\pi}$-mesons with spin 0 or 1 are responsible for nuclear forces does not. Although the smaller range for the nuclear forces thus obtained from the latter theory is not at variance with the high energy neutron-proton scattering experiment, deuteron quadrupole moment cannot be accounted for by a $\ensuremath{\pi}$-meson field alone, so that the admixture of another meson field with larger range is necessitated. Both $\ensuremath{\pi}\ensuremath{-}\ensuremath{\mu}$-decay and $\ensuremath{\mu}$-nuclear capture can be consistently accounted for by assuming spin \textonehalf{} for $\ensuremath{\mu}$-mesons as in Sakata theory. However, nuclear $\ensuremath{\beta}$-decay and $\ensuremath{\mu}\ensuremath{-}\ensuremath{\beta}$-decay have to be considered as direct processes as in Fermi's theory of $\ensuremath{\beta}$-decay, instead of indirect processes through virtual emission and absorption of $\ensuremath{\pi}$-mesons as assumed usually in the meson theory.