Recent Articles

RAPID COMMUNICATION

State-dependent equivalent local potentials for the Dirac equation

L. D. Miller

Phys. Rev. C 12, 710(R) (1975) - Published 1 August, 1975

Show Abstract

It is pointed out that previously published equivalent local representations of the relativistic Hartree-Fock exchange potentials are too small by a factor of 2. The implications of this error for the relativistic Hartree-Fock calculations of closed shell nuclei are discussed.

NUCLEAR STRUCTURE Dirac equation, equivalent local potentials presented.

RAPID COMMUNICATION

Particle-vibration resonances in neutron scattering from ${}^{208}{Pb}$

J. M. Ferguson

Phys. Rev. C 12, 713(R) (1975) - Published 1 August, 1975

Show Abstract

The ${}^{208}{Pb}$ total cross section below 600 keV is calculated by the coupled channel method. In this model the incident neutron is coupled to several ${}^{208}{Pb}$ vibrational levels. The $s$ -wave cross section including the resonance near 500 keV is well reproduced by the calculation. The model also predicts several narrow resonances with higher angular momentum.

NUCLEAR REACTIONS ${}^{208}{Pb} (n, n)$ ; $E = 0.2 - 0.7$ MeV; calculated $σ_{t} (ε)$ .

RAPID COMMUNICATION

32.1 ms isomer in ${}^{198}{Tl}$

P. Sen, N. Cue, and H. Bakhru

Phys. Rev. C 12, 716(R) (1975) - Published 1 August, 1975

Show Abstract

RAPID COMMUNICATION

Half-lives of ${}^{92 - 97}{Rb}$ and ${}^{142 - 145}{Cs}$

P. L. Reeder and J. F. Wright

Phys. Rev. C 12, 718(R) (1975) - Published 1 August, 1975

Show Abstract

Half-lives of ${}^{92 - 97}{Rb}$ and ${}^{142 - 145}{Cs}$ have been measured by counting $β$ particles emitted from sources deposited on the first dynode of an electron multiplier at the collector end of an online mass spectrometer. Decay curve analysis included corrections for growth and decay of daughter and granddaughter activities as well as for growth and decay of delayed-neutron products. These results differ from some earlier measurements at masses 93, 94, and 145. They confirm with equal or smaller uncertainties the recent half-life measurements done by direct counting of neutrons from those nuclides which are delayed neutron precursors.

RADIOACTIVITY ${}^{92, 93, 94, 95, 96, 97}{Rb}$ , ${}^{142, 143, 144, 145}{Cs}$ ; measured $T_{\frac{1}{2}}$ , on-line mass spectrometer, $β$ counting.

Erratum: Covariant pion - nucleus optical potential

L. Celenza, L. C. Liu, and C. M. Shakin

Phys. Rev. C 12, 721 (1975) - Published 1 August, 1975

Erratum: Reid soft-core potential and parity nonconserving effects in thermal-neutron capture by protons

Keith R. Lassey and Bruce H. J. McKellar

Phys. Rev. C 12, 721 (1975) - Published 1 August, 1975

Elastic and inelastic proton scattering from ${}^{21}{Ne}$ and $T = 1$ energy levels in ${}^{22}{Na}$

B. Chambon, P. Desgrolard, D. Drain, M. Lambert, and N. Persehaye

Phys. Rev. C 12, 1 (1975) - Published 1 July, 1975

Show Abstract

Excitation functions for the reactions ${}^{21}{Ne} (p, p)$ and ${}^{21}{Ne} (p, p^{'})$ were studied at eight angles for bombarding energies in the range $E_{p} = 0.6 - 2.0$ MeV. A total of 21 resonances was observed corresponding to ${}^{22}{Na}$ levels between 7.3 and 8.6 MeV excitation energy. The proton angular momenta are determined and spin and parity assignments are presented. Several new isobaric analog pairs in ${}^{22}{Na}$ and ${}^{22}{Ne}$ are also presented. Previous experimental and nuclear structure information is discussed.

NUCLEAR REACTIONS ${}^{21}{Ne} (p, p)$ , ( $p, p^{'}$ ), $E = 0.6 - 2.0$ MeV; ${}^{22}{Na}$ deduced resonances, $L_{p}$ , $π$ , $J$ , $T$ . Isobaric pairs. Enriched target.

Neutron resonance spectroscopy: ${}^{203, 205}{Tl}$

H. I. Liou, J. Rainwater, G. Hacken, and U. N. Singh

Phys. Rev. C 12, 102 (1975) - Published 1 July, 1975

Show Abstract

Results are presented for high resolution time of flight neutron spectroscopy measurements of samples of natural Tl metal and of samples enriched in ${}^{203}{Tl}$ and in ${}^{205}{Tl}$ . Plots of $σ_{t}$ vs $E$ are given to 160 keV. Below 20 keV all observed levels are identified by isotope, and as $s$ or $p$ , the orbital angular momentum of the interacting neutron. Values of $E_{0}$ and $g Γ_{n}$ are given for all observed levels, comprised of 25 $s$ and 11 $p$ levels in ${}^{203}{Tl}$ , and 5 $s$ and 6 $p$ levels in ${}^{205}{Tl}$ . Favored $J$ is given in many cases. Values of $Γ_{γ}$ for 6 $s$ levels in ${}^{203}{Tl}$ and 2 $s$ levels in ${}^{205}{Tl}$ give $〈 Γ_{γ} 〉 = 0.65$ eV for ${}^{203}{Tl}$ and 0.80 eV for ${}^{205}{Tl}$ . Above 20 keV, values of $E_{0}$ and $Γ$ ( $\approx Γ_{n}$ ) are given for 29 $s$ levels to 104 keV, with favored $A$ for 20 levels and favored $J$ for 16 levels. Values of $E_{0}$ and ( $ag Γ_{n}$ ) are given for 44 $p$ levels above 20 keV. Intermediate structure effects seem to be present for ${}^{203}{Tl}$ to give $Σ \frac{g Γ_{n}^{0}}{Δ E}$ below 6.6 keV much larger than for $6.6 keV < E < 20 keV$ . Ignoring that effect, a usual analysis for the results below 20 keV gives $10 {}^{4}S_{0} = ({1.28}_{- 0.31}^{+ 0.45})$ for ${}^{203}{Tl}$ and ( ${0.38}_{- 0.18}^{+ 0.44}$ ) for ${}^{205}{Tl}$ , with $10 {}^{4}S_{1} = ({0.25}_{- 0.09}^{+ 0.16})$ for ${}^{203}{Tl}$ and ( ${0.15}_{- 0.07}^{+ 0.14}$ ) for ${}^{205}{Tl}$ .

NUCLEAR REACTIONS ${}^{203, 205}{Tl} (n, n)$ , ( $n, γ$ ), $E = 15 eV - 104 keV$ ; measured $σ_{t} (E)$ to 160 keV; deduced $E_{0}$ , $l$ , $J$ , $g Γ_{n}$ or $ag Γ_{n}$ or $Γ$ , $S_{0}$ , $S_{1}$ .

Shape transitional aspects of odd- $A$ Eu isotopes studied by the ( $p, t$ ) reaction

H. Taketani, H. L. Sharma, and Norton M. Hintz

Phys. Rev. C 12, 108 (1975) - Published 1 July, 1975

Show Abstract

The abrupt shape transition as is observed around $N ≃ 88 - 90$ in even nuclei has been examined for the odd- $A$ Eu isotopes ${}^{151}{Eu}_{88}$ and ${}^{149}{Eu}_{86}$ by the ( $p, t$ ) reaction at 18.5 and 19.0 MeV with an average resolution of 10 keV. Angular distributions, taken from 10 to 70°, enabled unambiguous indentification of many $L = 0$ ( ${J_{f}}^{π} = \frac{5}{2^{+}}$ ) transitions in both residual nuclei; seven for ${}^{151}{Eu}$ and seven or eight for ${}^{149}{Eu}$ . The summed $L = 0$ cross sections are close to those of the ( $p, t$ ) reactions for the neighboring even- $A$ Sm isotopes connecting the same neutron numbers. A number of new levels have been found in both isotopes. We have obtained markedly different level structures for the two neighboring isoptopes. In ${}^{151}{Eu}$ , whose ground state and low-lying states below 200 keV can be described in terms of spherical shell-model configurations, two deformed bands have been tentatively identified. One of these is a $\frac{5}{2^{+}} [413]$ band with members at 261 keV, $\frac{5}{2^{+}}$ ; 414 keV, ( $\frac{7}{2^{+}}$ ); and possibly a 597 keV, ( $\frac{9}{2^{+}}$ ) member. In addition a $\frac{5}{2^{+}} [413]$ $β$ band is postulated with members at 654 keV, $\frac{5}{2^{+}}$ ; 801 keV, ( $\frac{7}{2^{+}}$ ). These deformed states, coexisting with the spherical states, have been strongly excited while the spherical low-lying states have shown vanishingly small ( $p, t$ ) cross sections. The ( $p, t$ ) cross sections to the ${}^{151}{Eu}$ states were found to be in strong anticorrelation with $B (E 2)$ values from Coulomb excitation and ( $d, d^{'}$ ) cross sections leading to the same final states. On the other hand, ${}^{149}{Eu}$ has shown the usual ( $p, t$ ) pattern of a strong ground state transition and weak excited state transitions, showing similar coupling schemes are involved in the ground states of ${}^{151}{Eu}$ and ${}^{149}{Eu}$ . The detailed experimental results up to 1.6 MeV excitation in both nuclei and their interpretation for some of the levels are presented.

NUCLEAR REACTIONS ${}^{153, 151}{Eu} (p, t)$ , $E = 18.5 and 19.0$ MeV; measured $σ (E_{t}, θ)$ , $Q$ . ${}^{151, 149}{Eu}$ deduced levels, $J$ , $π$ . Enriched targets.

C + ${}^{19}F$ reactions at $E_{lab} = 25 - 72$ MeV

A. F. Zeller, G. R. Choppin, H. S. Plendl, and C. I. Delaune

Phys. Rev. C 12, 124 (1975) - Published 1 July, 1975

Show Abstract

Thick targets of natural carbon were bombarded with ${}^{19}F$ ions at $E_{lab} = 25 - 72$ MeV. Residual activities were counted off-line with a Ge(Li) detector. $γ$ rays from the decay of ${}^{7}{Be}$ , ${}^{22}{Na}$ , ${}^{24}{Na}$ , ${}^{27}{Mg}$ , ${}^{28}{Mg}$ , ${}^{28}{Al}$ , and ${}^{29}{Al}$ were observed, and yield curves were determined. Yield curves calculated with the Blann-Plasil statistical evaporation code were compared with the experimental results and found to agree well in most cases.

NUCLEAR REACTIONS C + ${}^{19}F$ , $E = 25 - 72$ MeV; measured activation yields of ${}^{7}{Be}$ , ${}^{22}{Na}$ , ${}^{24}{Na}$ , ${}^{27}{Mg}$ , ${}^{28}{Mg}$ , ${}^{28}{Al}$ , and ${}^{29}{Al}$ . Natural targets, Ge(Li) detector.

Wave-packet aspects of high-momentum strongly absorbing nuclear reactions

N. Austern

Phys. Rev. C 12, 128 (1975) - Published 1 July, 1975

Show Abstract

Properties of the wave function associated with a simple parametrized expression for the transfer amplitude are discussed. Near the nuclear surface the wave function is localized in angle, but is not appreciably localized in radius. These results seem to contradict descriptions of reactions in terms of classical trajectories.

NUCLEAR REACTIONS Relation between $l$ localization and wave function localization discussed.

5.534 MeV level in ${}^{23}{Na}$

G. D. Jones, P. W. Green, D. T. Kelly, G. G. Frank, and J. A. Kuehner

Phys. Rev. C 12, 132 (1975) - Published 1 July, 1975

Show Abstract

The ${}^{12}C ({}^{12}C, p γ) {}^{23}{Na}$ reaction has been used at an incident energy of 28.2 MeV to populate the 5.534 MeV level in ${}^{23}{Na}$ . A particle $γ$ -ray linear polarization measurement carried out simultaneously with a particle $γ$ -ray angular correlation measurement for the 3.457 MeV transition between the 5.534 MeV and 2.077 MeV ( ${\frac{7}{2}}^{+}$ ) levels allows an unambiguous $J^{π} = {\frac{11}{2}}^{+}$ assignment to be made to the 5.534 MeV level. The multipole mixing ratio of the 2.829 MeV transition between the 5.534 MeV and 2.705 MeV ( ${\frac{9}{2}}^{+}$ ) levels has been obtained and confirms previous measurements, as does the measured branching ratio for the two observed decay modes from the 5.534 MeV level.

NUCLEAR REACTIONS ${}^{12}C ({}^{12}C, p γ)$ , $E = 28.2$ MeV; 5.534 MeV level, measured $P (E_{γ}, 90 °)$ , angular correlations, branching ratio, deduced $J$ and $Λ$ for transitions.

Heavy-ion optical potentials from few-nucleon transfer reactions

A. J. Baltz, P. D. Bond, J. D. Garrett, and S. Kahana

Phys. Rev. C 12, 136 (1975) - Published 1 July, 1975

Show Abstract

The sensitivity of forward angle heavy-ion transfer calculations to the details of the imaginary optical potential in the region of the nuclear surface is demonstrated. A phenomenological imaginary potential, consisting of a deep volume term of sharp diffusivity and a shallow surface term of standard diffusivity, is proposed and used in distorted-wave Born-approximation calculations to reproduce a variety of angular distribution shapes. The proposed parametrization of the imaginary potential allows the region of the nuclear surface to be transparent enough to produce large forward angle cross sections, seen experimentally, and yet remain strongly enough absorbing in the nuclear interior to suppress unphysical contributions from this region. Bound state configuration dependence of angular shapes, produced in two-particle transfer calculations with weakly absorbing volume potentials, is shown to be removed by the use of the proposed surface transparent potentials.

NUCLEAR REACTIONS DWBA analysis of $σ (θ)$ for ${}^{40}{Ca}$ ( ${}^{13}C$ , ${}^{14}N$ ), $E = 40$ MeV; ${}^{40}{Ca}$ ( ${}^{13}C$ , ${}^{12}C$ ), $E = 40, 60, and 68$ MeV; ${}^{48}{Ca}$ ( ${}^{14}N$ , ${}^{13}C$ ), $E = 50$ MeV; ${}^{60}{Ni}$ ( ${}^{18}O$ , ${}^{16}O$ ), $E = 65$ MeV; ${}^{60}{Ni}$ ( ${}^{18}O$ , ${}^{19}F$ ), $E = 65$ MeV. Discussion of optical-model parameters for such reactions.

Spectroscopic studies involving two-step processes in the reaction ${}^{28}{Si} (d, p) {}^{29}{Si} ({\frac{5}{2}}^{+})$

R. N. Boyd, J. Kaminstein, R. Arking, and H. Clement

Phys. Rev. C 12, 14 (1975) - Published 1 July, 1975

Show Abstract

Particle- $γ$ -ray angular correlations have been studied in the ${}^{28}{Si} (d, p) {}^{29}{Si} ({\frac{5}{2}}^{+}, 2.03 MeV)$ reaction and subsequent $γ$ -ray decay to the ${}^{29}{Si}$ ground state. The calculated correlations represent the data well near the stripping peak, and show appreciable sensitivity to the details of the two-step reaction processes. This sensitivity allows the determination of structure information about excited core components of the nuclear wave function.

NUCLEAR REACTIONS ${}^{28}{Si} (d, p γ)$ , $E = 7.6$ MeV; proto- $γ$ -ray angular correlations, ${}^{29}{Si}$ deduced effect of inelastic processes on angular correlations; natural target.

Estimation of total reaction cross sections from elastic scattering data

John M. Alexander, H. Delagrange, and A. Fleury

Phys. Rev. C 12, 149 (1975) - Published 1 July, 1975

Show Abstract

A study is made of the interaction distance parameters from sharp and smooth cutoff analysis of elastic scattering data. These distance parameters are compared to interaction barrier parameters from analysis of total-reaction-cross-section data. A simple method is proposed for calculation of total reaction cross sections from the empirical parameters.

NUCLEAR REACTIONS Systematics are given for the distance parameters from sharp and smooth cutoff analysis of elastic scattering data. A simple method is proposed for calculation of total reaction cross sections.

${}^{12}C ({}^{12}C, α) {}^{20}{Ne}$ excitation functions and angular distributions

L. R. Greenwood, R. E. Segel, K. Raghunathan, M. A. Lee, H. T. Fortune, and J. R. Erskine

Phys. Rev. C 12, 156 (1975) - Published 1 July, 1975

Show Abstract

Excitation functions have been measured at a laboratory angle of 5° over an incident energy range of 18-25.5 MeV (c.m.) for the ${}^{12}C ({}^{12}C, α)$ reaction leading to about 30 levels in ${}^{20}{Ne}$ ( $E_{x} = 0 - 20$ MeV). Angular distributions were measured at five energies. An Ericson fluctuation analysis yields the result that most levels are populated by a large nonstatistical reaction component. A significant compound-nuclear component is also present, with correlation widths on the order of 150-250 keV (c.m.). The energy-averaged cross sections have been compared with statistical compound-nuclear (Hauser-Feshbach) calculations. This comparison indicates the presence of a strong direct-reaction mechanism, especially for the members of the proposed 8p-4h band (at 7.196, 7.834, 9.040, and 12.16 MeV). A pronounced minimum in the excitation functions is evident at $E_{c . m .} = 19.2$ MeV, near the recently reported strong resonance in the ${}^{12}C ({}^{12}C, p) {}^{23}{Na}$ channel. Other correlated effects also appear to be present at specific energies, but the cross correlations, calculated for the entire energy range, are largely statistical.

NUCLEAR REACTIONS ${}^{12}C ({}^{12}C, α)$ , 5° yield curves $E_{{}^{12}C} 36 - 51$ MeV, angular distribution 37, 41, 45, 48, and 51 MeV, statistical analyses.

High-energy expansion for nuclear multiple scattering

Stephen J. Wallace

Phys. Rev. C 12, 179 (1975) - Published 1 July, 1975

Show Abstract

The Watson multiple scattering series is expanded to develop the Glauber approximation plus systematic corrections arising from three effects: (1) deviations from eikonal propagation between scatterings, (2) Fermi motion of struck nucleons, and (3) the kinematic transformation which relates the many-body scattering operators of the Watson series to the physical two-body scattering amplitude. Operators which express effects ignored at the outset to obtain the Glauber approximation are subsequently reintroduced via perturbation expansions. Hence a particular set of approximations is developed which renders the sum of the Watson series to the Glauber form in the center of mass system, and an expansion is carried out to find leading order corrections to that summation. Although their physical origins are quite distinct, the eikonal, Fermi motion, and kinematic corrections produce strikingly similar contributions to the scattering amplitude. It is shown that there is substantial cancellation between their effects and hence the Glauber approximation is more accurate than the individual approximations used in its derivation. It is shown that the leading corrections produce effects of order ${(2 k R_{c})}^{- 1}$ relative to the double scattering term in the uncorrected Glauber amplitude, $ℏ k$ being momentum and $R_{c}$ the nuclear charge radius. The leading order corrections are found to be small enough to validate quantitative analyses of experimental data for many intermediate to high energy cases and for scattering angles not limited to the very forward region. In a Gaussian model, the leading corrections to the Glauber amplitude are given as convenient analytic expressions.

NUCLEAR REACTIONS Multiple scattering theory at intermediate to high energy; leading corrections to Glauber approximation due to eikonal, Fermi motion, and kinematic effects.

Crossing, unitarity, and the impulse approximation in pion-nucleus scattering

L. Celenza, L. C. Liu, and C. M. Shakin

Phys. Rev. C 12, 194 (1975) - Published 1 July, 1975

Show Abstract

We present a theory of pion-nucleus scattering which incorporates crossing symmetry. The resulting nonlinear $T$ matrix equation is a generalization of the Low equation to the case of complex targets. If one neglects crossing symmetry in the formalism, the theory reduces to the linear theory of pion-nucleus scattering discussed previously. Our method requires the introduction of a non-Hermitian effective Hamiltonian (for the description of elastic scattering) whose definition is based on a projection operator technique. It is pointed out that one great advantage of our theory over other approaches which incorporate crossing symmetry lies in the fact that (in the simplest approximation) the driving term in our equation may be identified with the "triangle diagram," that is, the leading term in a covariant multiple scattering series for the relativistic optical potential. The approximations which are necessary to obtain familiar expressions for the driving term are made explicit in the context of this theory.

NUCLEAR REACTIONS Pion-nucleus scattering, crossing symmetry, optical model.

Pion-nucleus elastic scattering at intermediate energies

D. I. Julius and C. Rogers

Phys. Rev. C 12, 206 (1975) - Published 1 July, 1975

Show Abstract

Dynamical modifications of the pion-nucleus optical potential due to binding effects on the target nucleons are calculated for pions of energies in the range 120-600 MeV. Calculations are performed using an independent particle model for the nucleus; however, a prescription for incorporation of the Pauli principle is given and its effects are studied. Resulting corrections to the potential are of the order of 50-100% near the (3, 3) resonance and fall to negligible values at energies less than 120 MeV and greater than 450 MeV. Our correction is such as to increase the nuclear opacity. Pion-nucleus total cross sections and angular distributions are modified by binding effects by 10-20%. Comparison with $π$ - ${}^{12}C$ total cross section data shows that our theory reproduces well the energy dependence of the correction required to reconcile theory and experiment, and produces about 50% of the necessary increase in the magnitude of the theoretical cross section.

NUCLEAR REACTIONS ${}^{12}C (π, π)$ ; calculated $σ_{T} (E)$ , $E = 120 - 600$ MeV; binding corrections.

${}^{37}{Cl} (p, n) {}^{37}{Ar}$ excitation function up to 24 MeV: Study of ( $p, n$ ) reactions

R. Kishore, R. Collé, S. Katcoff, and J. B. Cumming

Phys. Rev. C 12, 21 (1975) - Published 1 July, 1975

Show Abstract

Cross sections for the ${}^{37}{Cl} (p, n) {}^{37}{Ar}$ reaction were determined from 2 to 24 MeV by the activation method. NaCl targets of natural isotopic composition were irradiated inside of Al cells having thin Havar windows. Beam intensities were determined with a Faraday cup and the ${}^{37}{Ar}$ disintegration rates were measured with internal gas proportional counters. The cross sections (±6% uncertainty) increase from threshold (1.64 MeV) to a broad maximum of 365 mb at 10 MeV and then decrease to 34 mb at 23.5 MeV. These results and five other recently measured ( $p, n$ ) excitation functions are compared with each other and with various cascade-evaporation calculations. Reasonable agreement was attained between experiment and calculation, and possible sources of remaining discrepancies are discussed. The ${}^{37}{Ar}$ half-life is observed to be 35.02±0.05 day, in good agreement with previously reported values.

NUCLEAR REACTIONS ${}^{37}{Cl} (p, n)$ , $E = 2 - 24$ MeV; measured $σ (E)$ . Natural targets, Faraday cup, internal gas proportional counters. RADIOACTIVITY ${}^{37}{Ar}$ ; measured $T_{\frac{1}{2}}$ .

Select page:

Physical Review C

Recent Articles

Filter

Recent Issues

State-dependent equivalent local potentials for the Dirac equation

Particle-vibration resonances in neutron scattering from ${}^{208}{Pb}$

32.1 ms isomer in ${}^{198}{Tl}$

Half-lives of ${}^{92 - 97}{Rb}$ and ${}^{142 - 145}{Cs}$

Erratum: Covariant pion - nucleus optical potential

Erratum: Reid soft-core potential and parity nonconserving effects in thermal-neutron capture by protons

Elastic and inelastic proton scattering from ${}^{21}{Ne}$ and $T = 1$ energy levels in ${}^{22}{Na}$

Neutron resonance spectroscopy: ${}^{203, 205}{Tl}$

Shape transitional aspects of odd- $A$ Eu isotopes studied by the ( $p, t$ ) reaction

C + ${}^{19}F$ reactions at $E_{lab} = 25 - 72$ MeV

Wave-packet aspects of high-momentum strongly absorbing nuclear reactions

5.534 MeV level in ${}^{23}{Na}$

Heavy-ion optical potentials from few-nucleon transfer reactions

Spectroscopic studies involving two-step processes in the reaction ${}^{28}{Si} (d, p) {}^{29}{Si} ({\frac{5}{2}}^{+})$

Estimation of total reaction cross sections from elastic scattering data

${}^{12}C ({}^{12}C, α) {}^{20}{Ne}$ excitation functions and angular distributions

High-energy expansion for nuclear multiple scattering

Crossing, unitarity, and the impulse approximation in pion-nucleus scattering

Pion-nucleus elastic scattering at intermediate energies

${}^{37}{Cl} (p, n) {}^{37}{Ar}$ excitation function up to 24 MeV: Study of ( $p, n$ ) reactions

Filter

Recent Issues

Filter

Article Lookup

Enter a citation