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A nuclear isomer is a metastable state of an atomic nucleus, in which one or more nucleons (protons or neutrons) occupy higher energy levels than in the ground state of the same nucleus. "Metastable" describes nuclei whose excited states have half-lives 100 to 1000 times longer than the half-lives of the excited nuclear states that decay with a "prompt" half life (ordinarily on the order of 10−12 seconds). The term "metastable" is usually restricted to isomers with half-lives of 10−9 seconds or longer. Some references recommend 5 × 10−9 seconds to distinguish the metastable half life from the normal "prompt" gamma-emission half-life. Occasionally the half-lives are far longer than this and can last minutes, hours, or years. For example, the nuclear isomer survives so long (at least 1015 years) that it has never been observed to decay spontaneously. The half-life of a nuclear isomer can even exceed that of the ground state of the same nuclide, as shown by as well as , , and multiple holmium isomers. Sometimes, the gamma decay from a metastable state is referred to as isomeric transition, but this process typically resembles shorter-lived gamma decays in all external aspects with the exception of the long-lived nature of the meta-stable parent nuclear isomer. The longer lives of nuclear isomers' metastable states are often due to the larger degree of nuclear spin change which must be involved in their gamma emission to reach the ground state. This high spin change causes these decays to be forbidden transitions and delayed. Delays in emission are caused by low or high available decay energy. The first nuclear isomer and decay-daughter system (uranium X2/uranium Z, now known as /) was discovered by Otto Hahn in 1921. The nucleus of a nuclear isomer occupies a higher energy state than the non-excited nucleus existing in the ground state. In an excited state, one or more of the protons or neutrons in a nucleus occupy a nuclear orbital of higher energy than an available nuclear orbital.
[2]Paolo Prandoni, [3]LCAV, EPFL
The Karplus-Strong algorithm is a simple method to generate synthetic
sounds with arbitrary pitch. In this notebook we will explore a few
variations of the method to illustrate some basic notions of
discrete-time signal processing.
In [1]:
%matplotlib inline
import matplotlib
import matplotlib.pyplot as plt
import numpy as np
import IPython
In [2]:
plt.rcParams["figure.figsize"]