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The extra power of r causes a quadratically faster decrease of the matrix elements with l, as can be seen from the analytical expression 31 of the radial diagonal matrix elements of (Formula presented)
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The extra power of r causes a quadratically faster decrease of the matrix elements with l, as can be seen from the analytical expression 31 of the radial diagonal matrix elements of (Formula presented).
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43
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85037204380
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See Ref. 31, Sec. 60, Eqs. (60.7) and (60.11) in particular
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See Ref. 31, Sec. 60, Eqs. (60.7) and (60.11) in particular.
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85037241715
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The distance of closest approach at high n's is l(l+1)/2
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The distance of closest approach at high n's is l(l+1)/2.
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54
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85037199284
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When, for a neutral molecule, additional, dipole bound states are possible 55,56
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When, for a neutral molecule, additional, dipole bound states are possible 55,56.
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36449004510
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85037188701
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Since the difference between the two-density of states is a function of the rotational constant B of the core, we can use one coupling constant and B
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Since the difference between the two-density of states is a function of the rotational constant B of the core, we can use one coupling constant and B.
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59
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85037219949
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The only way to further increase the density of accessible states is to break M as a good quantum number by imposition of an external magnetic field 17–19 or by the presence of other ions 12,20,23
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The only way to further increase the density of accessible states is to break M as a good quantum number by imposition of an external magnetic field 17–19 or by the presence of other ions 12,20,23.
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60
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85037200519
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To see the transition from local to average behavior of the coupling constant, consider the density of states within a Stark manifold. Then δE=3nF. At the Inglis-Teller limit γ=(Formula presented)
-
To see the transition from local to average behavior of the coupling constant, consider the density of states within a Stark manifold. Then δE=3nF. At the Inglis-Teller limit γ=(Formula presented).
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61
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85037216366
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The variation in the weight from one eigenstate to another is what one would expect for quantum fluctuations in the strong-coupling limit in the two-series problem 62
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The variation in the weight from one eigenstate to another is what one would expect for quantum fluctuations in the strong-coupling limit in the two-series problem 62.
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65
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85037184047
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This means that the Hamiltonian is symmetric and can be diagonalized by an orthogonal transformation, unlike the situation when the continuum is energetically accessible. One can then use an effective Hamiltonian within the bound subspace 63,64, which needs to be diagonalized in a biorthogonal basis
-
This means that the Hamiltonian is symmetric and can be diagonalized by an orthogonal transformation, unlike the situation when the continuum is energetically accessible. One can then use an effective Hamiltonian within the bound subspace 63,64, which needs to be diagonalized in a biorthogonal basis.
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68
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85037183713
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This delay is necessary to remove the promptly produced ions
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This delay is necessary to remove the promptly produced ions.
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70
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0003851731
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