This python library can be used to calculate angular distributions/correlations.
To use the library, the following dependencies have to be fullfilled:
- python≥3.6
- sympy
To run the tutorial notebook, matplotlib is required.
To calculate the ϑ-, φ- and δ-dependent angular correlation of a 0⁺ → 1⁻ → 0 cascade, use the following code:
from sympy import Symbol
from angcorrwat import W
theta = Symbol('theta')
phi = Symbol('phi')
delta = Symbol('delta')
W(theta, phi, [0, 1], [1, 0, 0], [[0, delta]])
The resulting angular distribution is normalized to 1, when integrated over the solid angle. The incident γ-ray beam is assumed to be linearily polarized. Spherical coordinates are used: While the azimuthal angle φ refers to the angle between the polarization plane and the reaction plane, the polar angle ϑ is given with respect to the incident γ-ray. For the multipole mixing ratio δ, the convention by Krane, Steffen and Wheeler [2] is used.
The arguments theta and phi refer to the respective spherical coordinates ϑ and φ.
The third argument [0, 1] = [J, π] refers to the initial state Jπ = 0+ (0 is negative and 1 positive parity).
The fourth argument [1, 0, 0] = [J, π, δ] refers to the state (de)excited by the first γ, with δ refering to the multipole mixing ratio for the transition between the initial and excited state.
Finally, a list of states [[J, δ], …] of the subsequent cascade is given, with δ refering to the multipole mixing ratio for the transition between the previous and current state.
The angular distribution of the final state in the cascade is returned.
For more examples, take a look at the tutorial (launch in binder).
© 2018– O. Papst <[email protected]>
angcorrwat is distributed under the terms of the GNU General Public License, version 3 or later.
See the LICENSE file.
We thank U. Friman-Gayer and C. Iliadis for valuable discussions. This work has been funded by the State of Hesse under the grant “Nuclear Photonics” within the LOEWE program. O. Papst acknowledges support by the Helmholtz Graduate School for Hadron and Ion Research of the Helmholtz Association.
[1] R. M. Steffen et al., “Angular distribution and correlation of gamma rays”, in The electromagnetic interaction in nuclear spectroscopy, edited by W. D. Hamilton (North-Holland, Amsterdam, 1975) Chap. 12, pp. 505–582, ISBN: 978-0-4441-0519-6.
[2] K. S. Krane et al., “Directional correlations of gamma radiations emitted from nuclear states oriented by nuclear reactions or cryogenic methods”, At. Data Nucl. Data Tables 11, 351 (1973). doi:10.1016/S0092-640X(73)80016-6.
[3] L. C. Biedenharn and M. E. Rose, “Theory of angular correlation of nuclear radiations”, Rev. Mod. Phys. 25, 729 (1953). doi:10.1103/RevModPhys.25.729.