Wavelengths and Energy Levels of Neutral Kr84 and Level Shifts in All Kr Even Isotopes.

Interferometrically-measured wavelengths of 109 lines of neutral Kr84 are compared with those of Kr86. Sixty energy levels of neutral Kr84 derived from those wavelengths and 25 Kr86-Kr84 isotope shifts previously measured are given along with their shifts from the energy levels of Kr86. Twenty levels of each of Kr82, Kr80, and Kr78 are also evaluated using isotope-shift information in the literature. The differences between the experimentally observed shifts and the normal mass shift leave large negative residuals which are accounted for by ionization energy differences and by the specific mass shift. It appears that the volume effect causes only a very small, if any, energy level shift.


Introduction
In 1969, Kaufman and Humphreys [1] determined a set of 45 even-parity and 66 odd-parity levels of neutral Kr*** based upon interferometrically-determined wavelengths of that isotope of krypton. The energies relative to the ground level, based on the vacuum-ultraviolet observations of Petersson [2], had an absolute uncertainty of ±0.15 cm"', although their relative uncertainties were much smaller. (All uncertainties in this paper are one standard deviation estimates unless otherwise stated.) Trickl et al. [3], in 1989, measured the values of the resonance lines of Kr^ from four of the 7 = 1 levels of the 4p^5s, 6s, and 7s configurations with an average uncertainty of 1 part in 10'. Their results led to a subtraction of (0.0679±0.0061) cm'' from the values given by Kaufman and Humphreys [1]. This correction was incorporated in the compilation of the energy levels by Sugar and Musgrove [4]. electrodeless discharge lamp maintained in a bath of nitrogen at its triple-point temperature, was used as the wavelength standard. The Kr** spectrum was observed from a similarly cooled, microwave-excited electrodeless lamp. Both lamps were viewed along the capillary. Interferometer spacers of 50 mm, 80 mm, and 100 mm were used, but final corrections for dispersion of phase change were taken from the more extensive data of C. J. Humphreys.
The 109 interferometricaliy measured vacuum wavelengths of Kr** are given in the first column of Table 1. Also included in the table are the wavelength uncertainties in parentheses (in units of the last digit) and wavenumbers of the Kr" lines, the Kr*' wavelengths and wavenumbers for those same 109 lines from Ref. [1], the classification of each transition and the wavenumber difference between the two isotopes. The wavelength uncertainties are the rms deviations in the set of measurements for each line.    *" Wavenumber of the Kr"* transition minus that of the Kr** transition in units of 10"^ cm"'. The uncertainty of the last digit of the Kr* measurement is given in parentheses for those transitions for which direct isotope shift measurements are available. 'In units of 10"^ cm"'. '' Direct (&"*-&*") isotope shift measurement by Ref. [6]. The uncertainty of the measurement is given in parentheses. ' Direct (Kr*'-Kr'") isotope shift measurement by Ref. [7]. The uncertainty of the measurement is given in parentheses. 'Direct (&"*-&**) isotope shift measurement by Ref. [8]. The uncertainty of the measurement is given in parentheses. » Direct (Kr'^-Kr**) isotope shift measurement by Ref. [9]. The uncertainty of the measurement is given in parentheses. " Direct (Kr^^-Kr'") isotope shift measurement by Ref. [10]. The uncertainty of the measurement is given in parentheses. ' Direct (Kr'**-Kr'") isotope shift measurement by Ref. [11]. The uncertainty of the measurement is given in parentheses. ' Direct (KT**-Kr'") isotope shift measurement by Ref. [12]. The uncertainty of the measurement is given in parentheses. " Direct (Kr"*-Kr*') isotope shift measurement by Ref. [13]. The uncertainly of the measurement is given in parentheses.
A number of investigators [6][7][8][9][10][11][12][13] have made direct measurements of isotope shifts between Kr** and Kr^. These are also given in Table 1. Direct measurements, by their very nature, are much more accurate than the difference between two completely independent measurements. This is evident in the stated uncertainties following both the differences, Au, and the direct isotope separations in Table 1. However, it should be noted that there is agreement within the stated uncertainties in most cases.

Energy Levels of Kr"
Trickl et al. [3] also measured the isotope shifts in the aforementioned four vacuum-ultraviolet lines for several of the isotopes of krypton, including those between Kr** and Kr*"*. Without those measurements, it would not be possible to give separate values for the energy levels of the two isotopes relative to the ground level.
With the aid of the same iterative level-calculation program used in Ref. [1], the 109 wavenumbers of Kr** given in Table 1 were combined with the Kr'^-Kr*' isotope shift measurements from Refs. [6][7][8][9][10][11][12][13] and with the vuv values for Kr^ from Ref. [3] to determine the Kr** energy-level values. Table 2 includes these newly determined values with their uncertainties (in units of the last digit) in parentheses. Also included are the Kr"* values for these same levels from the work of Kaufman and Humphreys [1], the Kr^-Kr*" differences and the number of transitions to or from each Kr'" level included in the 109 wavelength measurements.
Jackson [6,13] measured wavenumber shifts between pairs of the five stable even isotopes of krypton in fifteen 5s-5p lines, six 5s-6p lines, and one 5p-6d line. Champeau and Keller [8] did the same for two other 5s-5p transitions and one 5s-6p transition for all but the Kr™ isotope. Further information on four of these 25 lines can be found in Refs. [7] and [9][10][11][12], Combining these previously reported data with the vuv high resolution measurements of the isotope shifts between Kr*^ and each of Kr'^ Kr«", and Kr™ given by Trickl et al. [3] for the 4p'-4p' CP°,a)5s 2[l/2]°, transition, it is possible to evaluate a total of 20 excited levels in each of these isotopes. These values are given in Table 3. The isotope shifts of these levels with respect to those of Kr"* are also given. .7511(2) 6.9 .3120 (2) .6214 (7) 7. .6333 (2) .9140 (7) 6 ■The difference between the level values of the two isotopes is given in units of 10"' cm"'.
'' The number in this column indicates the number of intcrferometrically measured lines with transitions to or from that level. Discussions of the two effects, the finite mass of the nucleus and the non-zero nuclear volume, which lead to the observation of isotope shifts are discussed in some detail in Refs. [3, 6 and 13]. In all of those instances, the authors point out that the difference between the experimentally observed isotope shift of a line, Avdiff, and the normal mass shift, Afnm, is accounted for by the sum of the specific mass shift, Aj/sm, and the shift due to the volume effect, A^,oi. We now have the opportunity to discuss the difference in the term values of the levels of isotopes. The term value T is defined as the binding energy of the electron, i.e., T = IE -(Level value). Here IE is the energy of the appropriate Kr ii 4p^^P°3a or ^F'm level with respect to the Kr i 4/>* 'So ground level, which has been taken as zero for each isotope. The normal mass shifts of the term values of levels near the ionization limit approach zero and increase with increasing term value of a level. The values of Ai'nm for the corresponding term-value differences are given for Kr'^-Kr*' in column 4 of Table 2 and for Kr^-Kr*^ Kr«*-Kr^ and Kr**-Kr™ in Table 3. They show that the differences in binding energies of the 4/?* 'So ground states due only to the normal mass effect are 17.0x 10-\ 34.9xl0-\ 53.6x]0-^ and 73.3x10"' cm"', respectively for Kr**, Kr*^ Kr*", and Kr'* with respect to Kr**.
For any two isotopes Ar"p = A(/£)-Avi" = AVnm + AVsm+Ai'vol (1) where ATcxp is the observed shift in the term value. Thus by adding the experimentally observed isotope shift A Via and the calculated normal mass shift Av"m for term values of levels relatively close to the ionization limit, where the specific mass and volume effects must be negligible, we can find values of the differences in the 4pM/7"P° ionization energies of these isotopes. The addition of columns 3 and 4 of Table 2 for Kr^'^-Kr*' and the equivalent columns in Table 3 for the other three krypton pairs, gives ionization energy differences with estimated uncertainties of ±0.5xl0~' cm"' of these four isotopes from Kr^. They are 7.5xl0-^ 15.6xl0-^ 24.1xl0"^ and 32.4x10"' cm"', respectively for Kr**, K^*^ Kr^, and Kr™. By definition, these are the experimental differences between the binding energies of a 4p electron in the ground level of these respective isotopes and the same binding energy for the Kr** isotope. Table 4 gives the term value shifts due to the sum of the specific mass and volume effects as obtained by applying Eq. (1) to the 4^" 'So and the other twenty levels given in Table 3 and the same levels in Table 2. The estimated uncertainty of ±0.6x10"' cm"' for term value shifts is due to both the estimated uncertainty of ±0.5 x 10"' cm"' on the ionization energy differences given above and an uncertainty of about 0.2 x 10"' cm"' on the value of the isotope shifts. Table 4. Term-value shifts, in units of lO"' cm"', due to the sum of the specific mass and volume effects