The Absorption Spectra of Krypton and Xenon in the Wavelength Range 330–600 Å

Abstract

A total of 153 krypton resonances in the spectral region 330–500 Å and 253 xenon resonances in the spectral region 375–600 Å are reported. A detailed listing of the resonances is given, with wavelength and line shape information. The analysis of the spectra is very incomplete and will require detailed theoretical calculation to significantly improve it. In Kr, 45 resonances and in Xe, 56 resonances have been grouped into probable Rydberg series, for which classifications are suggested. The resonances are due, in the main, to either the excitation of the inner subshell “s” electron (s²p⁶ → sp⁶np) or to the excitation of two of the outer “p” electrons simultaneously (s²p⁶ → s²p⁴nln′l′). These high-lying excited states autoionize, resulting in resonances with window-, asymmetric-, or absorption-type profiles. Where possible, comparisons are made with previous work.

1. Introduction

This communication is intended as the final report on the absorption spectra of the noble gases He through Xe, observed in the wavelength range 80–600 Å. Earlier papers have dealt with the discovery and analysis (in some cases tentative) of the structure in the photoionization continuua of He[1],¹ Ne[2], and Ar[3]. We present here the spectra of Kr and Xe in the wavelength range 330–600 Å. Two previous publications have described the structure observed between 80 and 200 Å, due to the excitation of a single inner-shell d electron[4] and also the simultaneous excitation of an outer-shell p and an inner-shell d electron[5]. (The excitation of the outer p electron had been observed many years before [6].)

In the wavelength range 400–500 Å, Samson [7] observed two distinct resonances in the photoionization continuum of Kr using a many-lined spark discharge as a background source. Subsequently, many more autoionizing states in both Kr and Xe between 380 and 600 Å were reported [8] and recently, highlights of the present, more detailed experimental observations of the Kr and Xe spectra have been published [9]. In an accompanying paper [10], absolute cross-section measurements were made in the region of some of the more prominent resonances.

The following analysis of the Kr and Xe spectra is necessarily far from complete. The breakdown of strict L–S coupling, evident throughout the Ar spectrum, is even more pronounced in Kr and Xe. Consequently, considerable theoretical work is required, of an ab initio type, before a reasonable analysis of the Kr and Xe spectra can be made. In the hope of stimulating such calculations on noble gas atoms, we present here final numbers on wavelengths of the resonances observed, along with a rough guide as to the profiles of some of the resonances. The accompanying spectra and densitometer traces together with the published resonance profiles [10] may be helpful in comparing theoretical predictions with the experimental observations, at least for the low-lying levels.

2. Experimental Procedure

The spectra shown in figure 1 were taken using a three-meter grazing-incidence spectrograph [11]. The grating of 600 lines per mm and a 0.01 mm spectrograph entrance slit yielded a resolution of 0.06 Å. The source of continuum was provided by the radiation emitted by the NBS–SURF (Synchrotron Ultraviolet Radiation Facility). For this synchrotron the radiated power per unit wavelength peaks at 335 Å. Spectra were photographed from 80–600 Å with a grating blazed at 200 Å. The noble gas filled the spectrograph at pressures typically in the range of 0.01 to 0.10 torr, with absorption path lengths between entrance slit and plate of the order of 1 m. Since the synchrotron continuum is free from overlying emission and absorption lines, any features observed were due to the gas itself.

Figure 1. Upper Spectrum. The absorption spectrum of Kr between 345 and 500 Å, taken at two different pressures to accentuate the various regions of the spectrum.

(The background continuum cross section varies by over a factor of 3 through this region.) Black denotes absorption and therefore the prominent series of resonances due to the excitation of the subshell 4s electron to outer p orbitals are of the “window” type. The remaining resonances are due to the simultaneous excitation of two 4p electrons. Such resonances, grouped in series B, C, F, and G, are listed in table 3.

Lower Spectrum. The absorption spectrum of Xe between 425 and 600 Å, taken at three different pressures.

(The background continuum cross section varies by over a factor of 4 in this region). The prominent series of “window” resonances labeled A, are due to the excitation of a subshell 5s electron to outer p orbitals. Short series labeled C, D, and I are due to simultaneous excitation of two 5p electrons and are listed in table 4.

The spectra were photographed on Eastman SWR plates.² Wavelength calibration was obtained by super-imposing the absorption spectrum of He on the Kr and Xe spectra and by using the previously determined fact that wavelengths could be reliably predicted, by application of the grating equation, to an accuracy of at least 0.01 Å. As an additional check, where long Rydberg series existed, use was made of the fact that such series converge in the limit to a well established state of Kr ii or Xe ii. In the cases where only small perturbations exist good quantum defects were obtained using known limits and the measured wavelengths of the Rydberg series lines.

3. Classification of Spectra

The ground state of Kr is 4s²4p^{6 1}S₀, that of Xe 5s²5p^{6 1}S₀. The ionization potentials of Kr and Xe are 14.0 and 12.1 eV respectively. Thus, when photons of an energy between 20 and 40 eV are incident upon these gases, the basic process observed is photoionization. However, as well as exciting an outer p electron to continuum ϵs and ϵd states, it is possible to excite a subshell s electron to p-type orbitals or excite two electrons simultaneously. In the latter case, either two outer p electrons or both an outer p and a subshell s electron can be excited.

Thus, in Kr for example, one may excite to configurations of the type: 4s4p⁶np and 4s²4p⁴nln′l′ where ll′ = sp, pd, sf, df. Transitions of the type 4s4p⁵nln′l′ where ll′ = ss, pp, sd etc., have not been positively identified in Kr and Xe, although unidentified resonances exist in the appropriate energy region, and the existence of similar excitations has been fairly well established in Ar [3].

The total line list of 153 resonances in Kr and 253 resonances in Xe are listed in terms of their wavelength, wavenumber and resonance type in tables 1 and 2. By resonance type we mean the following. When a high-lying discrete state such as the 4s4p⁶5p state of Kr is excited by photoabsorption, the lifetime of this excited state is extremely short (~ 10⁻¹³ s). The state decays into the adjacent continuum by autoionization, with the ejection of an energetic electron, the ion being left in its ground or excited state. The interaction of a discrete state with the continuum of states of similar energy and parity has been dealt with by Fano and Cooper [12]. The resonances in the continuum which result from this interaction may be broad, and can have a variety of profiles.

Table 1. Code number, wavelength (λ), wave number (ν), and profile type for all observed Kr resonances, listed in order of decreasing wavelength.

Number	Wavelength (Å)	Wave number (cm−1)	Commenta
1	b501.23 ± .05	199509	-sx
2	498.83 ± .05	200469	−dw
3	c*497.50 ± .05	201005	+dw
4	496.90 ± .05	201248	dw
5	*496.07 ± .05	20l584	-dw
6	492.52 ± .05	203037	-sw
7	488.71 ± .05	204620	-dx’
8	488.06 ± .05	204893	-dx
9	472.26 ± .03	211748	+sw
10	*471.48 ± .03	212098	+sw
11	*471.23 ± .03	212211	-sw
12	469.08 ± .03	213183	-sx
13	464.70 ± .10	215193	-sw
14	*462.71 ± .03	216118	+sw
15	461.83 ± .03	2160530	-sx
16	460.405 ± .03	217179	sa
17	459.91 ± .03	217434	-sa
18	*458.69 ± .03	218012	+sw
19	457.86 ± .03	218407	-sw
20	457.51 ± .03	218574	sa
21	456.67 ± .03	218976	sa
22	*456.12 ± .03	219241	sw
23	455.29 ± .03	219640	−sx
24	*454.73 ± .03	219911	sw
25	454.01 ± .03	220259	sa
26	*453.73 ± .03	220395	sw
27	*453.l5 ± .03	220677	sw
28	*452.68 ± .03	220907	sw
29	*452.34 ± .03	221073	sw
30	*452.07 ± .03	221205	sw
31	451.98 ± .03	221249	sw
32	*451.86 ± .03	221307	sw
33	*451.69 ± .03	221391	sw
34	*451.56 ± .03	221455	sw
35	*451.45 ± .03	221508	sw
36	450.16 ± .03	222143	-sw
37	449.93 ± .03	222257	+sw
38	449.22 ± .03	222608	-sw
39	448.29 ± .03	223070	+sw
40	446.54 ± .05	223944	-sx
4l	444.02 ± .03	225215	+ sX
42	439.00 ± .2	227790	dw
43	434.30 ± .05	230256	-dw
44	433.98 ± .05	230425	sw
45	427.15 ± .03	234110	sa
46	426.53 ± .05	234450	-da
47	425.33 ± .07	235112	da
48	424.05 ± .05	235821	dw
49	423.61 ± .05	236066	sw
50	423.17 ± .07	236312	dw
5l	422.58 ± .03	236642	sa
52	421.56 ± .03	237214	—sx
53	421.23 ± .03	237400	—sx
54	420.90 ± .05	237586	—sx
55	420.36 ± .05	237891	-da
56	419.96 ± .05	238118	sa
57	419.74 ± .05	238243	Sa
58	419.51 ± .05	238373	sa
59	419.10 ± .10	238607	da
60	418.83 ± .03	238760	sw
61	418.70 ± .03	238834	sw
62	418.33 ± .05	239046	sa
63	*417.96 ± .03	239257	sa
64	*417.62 ± .03	239452	sa
65	*417.39 + .05	239584	sa
66	*417.22 ± .05	239682	sa
67	416.76 ± .05	239946	sw
68	416.01 ± .10	240379	dw
69	d14.78 ± .10	241092	sw
70	413.58 ± .10	241791	sw
71	412.79 ± .05	242254	+sw
72	412.47 ± .05	242442	sw
73	409.70 ± .2	244081	dda
74	406.85 ± .10	245791	da
75	405.30 ± .10	246731	da
76	403.34 ± .05	247930	da
77	401.50 ± .2	249070	dda
78	400.33 ± .07	249794	da
79	399.75 ± .07	250156	da
80	399.30 ± .10	2S0438	da
81	396.77 ± .10	252035	-dw
82	394.24 ± .07	253653	da
83	393.50 ± .07	254130	da
84	392.70 ± .07	254647	da
85	391.83 ± .05	255213	da
86	*391.44 ± .005	255467	sa
87	*390.49 ± .05	256088	da
88	390.04 ± .05	256384	sa
89	*389.48 ± .005	256753	da
90	*388.84 ± .005	257175	da
91	*388.37 ± .05	257486	sa
92	*388.05 ± .005	257699	sa
93	*387.79 ± .05	257872	sa
94	*387.60 ± .05	257998	sa
95	387.45 ± .005	258098	sa
96	*387.08 ± .05	258345	-da
97	386.26 ± .005	258893	-da
98	385.45 ± .07	259437	sa
99	*385.03 ± .05	259720	-sw
100	384.38 ± .05	260159	sa
101	*384.03 ± .05	260396	-sw
102	383.47 ± .05	260777	sa
103	383.22 ± .05	260947	sa
104	382.95 ± .05	261131	sa
105	d 382.45 ± .05	261472	da
106	382.07 ± .05	261732	sa
107	381.87 ± .05	261869	sa
108	381.51 ± .05	262116	sa
109	381.31 ± .05	262254	sa
110	380.80 ± .05	262605	sa
111	379.30 ± .2	263640	dda
112	*378.97 ± .05	263873	sa
113	*378.65 ± .05	264096	sa
114	*378.43 ± .05	264250	sa
115	*378.23 ± .05	264389	sa
116	375.03 ± .2	265390	dda
117	5.03 ± .05	266645	sa
118	374.66 ± .05	266909	sa
119	374.20 ± .05	267237	sa
120	373.00 ± .2	268100	dda
121	371.86 ± .05	268918	sa
122	371.37 ± .05	269273	sa
123	*370.87 ± .05	269636	sa
124	*370.13 ± .05	270175	sw
125	*369.13 ± .05	270907	sa
126	*368.60 ± .05	271297	sw
127	*368.14 ± .05	271636	sa
128	*367.56 ± .05	272064	+sa
129	*367.03 ± .05	272457	+sa
130	*366.70 ± .05	272702	+sa
131	*366.49 ± .05	272859	+sa
132	365.50 ± .2	273600	dda
133	363.80 ± .2	274880	dda
134	362.70 ± .2	275710	sa
135	362.30 ± .2	276010	sa
136	361.90 ± .2	276320	sa
137	359.60 ± .2	278090	sa
138	358.20 ± .2	279170	sa
139	357.30 ± .2	279880	sa
140	356.50 ± .2	280500	sa
141	d355.60 ± .2	281210	da
142	354.80 ± .2	281850	da
143	354.40 ± .2	282170	da
144	350.30 ± .2	285470	da
145	349.30 ± .2	286290	da
146	348.30 ± .2	287110	da
147	347.00 ± .2	288180	da
148	345.10 ± .2	289770	dda
149	343.50 ± .2	291120	da
150	342.30 ± .2	292140	sa
151	341.80 ± .2	292570	sa
152	341.10 ± .2	293170	sa
153	337.40 ± .3	296380	da

^aSign plus (+) or minus (−) represents the sign of q in the Fano [12] representation of noninteracting resonances. The letters s, d, dd, give a very rough idea of the sharpness or diffuseness of lines on a photographic plate. Naturally, this apparent width varies with gas pressure. The letters x, w or a indicate specifically if the resonance has been measured at (x) the point of highest rate of change of plate density, (w) the point of maximum plate density, or (a) the point of minimum plate density (maximum absorption); e.g., sw means a sharp resonance of low unknown (q) measured at the peak transmission point.

^bErrors shown represent the estimated absolute uncertainty. In the case of Kr the relative accuracies are of the order of 0.02 Å better than the estimated absolute uncertainty.

^cResonances denoted by an asterisk (*) are listed in table 3 as possible members of Rydberg series.

^dPossible double resonance.

Table 2. Code number, wavelength (λ), wave number (ν), and profile type for all observed Xe resonances, listed in order of decreasing wavelength.

Number	Wavelength(Å)	Wave number (cm−1)	Commenta
1	b 599.99 ± .05	166669	sw
2	595.93 ± .03	167805	-sw
3	c* 591.77 ± .03	168985	+dw
4	589.54 ± .02	169624	-sw
5	586.29 ± .02	170564	-sw
6	582.74 ± .02	171603	-sx
7	581.11 ± .02	172084	sw
8	579.98 ± .02	172420	sw
9	579.16 ± .02	172664	-sw
10	570.79 ± .02	175196	sw
11	570.47 ± .05	175294	sw
12	562.39 ± .02	177813	sa
13	560.64 ± .05	178368	-sa
14	560.44 ± .05	178431	+sa
15	558.78 ± .02	178961	-sx
16	* 557.83 ± .02	179266	+sw
17	556.51 ± .02	179691	+sx
18	555.52 ± .02	180012	-sw
19	555.28 ± .02	180089	sw
20	552.31 ± .02	181058	+sx
21	552.00 ± .02	181159	sw
22	* 550.76 ± .02	181567	+sx
23	549.60 ± .02	181951	sa
24	549.19 ± .05	182086	sa
25	548.14 ± .02	182435	sa
26	547.79 ± .02	182552	sa
27	546.88 ± .02	182855	sa
28	* 546.08 ± .02	183123	+sw
29	545.26 ± .02	183399	sw
30	544.95 ± .05	183503	sa
31	* 544.18 ± .02	183763	—sx
32	543.89 ± .02	183861	+sw
33	543.49 ± .05	183996	sw
34	541.95 ± .02	184519	sa
35	d 541.46 ± .05	184686	Sa
36	540.62 ± .02	184973	sw
37	* 540.54 ± .02	185000	sw
38	* 539.33 ± .02	185415	—sx
39	537.75 ± .02	185960	sa
40	* 537.46 ± .02	186060	sw
41	537.38 ± .02	186088	sw
42	537.22 ± .02	186143	sw
43	536.83 ± .02	186279	—sw
44	535.95 ± .02	186585	—sa
45	* 535.55 ± .02	186724	sw
46	535.13 ± .02	186870	—sx
47	* 534.58 ± .02	187063	—sx
48	* 534.27 ± .02	187171	sw
49	d* 533.34 ± .05	187498	sw
50	533.00 ± .02	187617	—sw
51	* 532.76 ± .02	187702	sw
52	532.06 ± .02	187949	—sw
53	531.83 ± .02	188030	-sw
54	* 531.37 ± .02	188193	-sw
55	* 531.21 ± .02	188249	sw
56	531.04 ± .02	188310	sw
57	* 530.93 ± .02	188349	sw
58	* 530.83 ± .03	188384	sw
59	*530.74 ± .03	188416	sw
60	530.10 ± .02	188644	-sw
61	529.94 ± .03	188701	sw
62	* 529.34 ± .02	188914	sw
63	528.93 ± .03	189061	sa
64	* 528.42 ± .03	189243	+sa
65	* 528.05 ± .05	189376	+sw
66	526.35 ± .02	189988	-sw
67	526.15 ± .02	190060	sw
68	525.86 ± .02	190165	sw
69	* 525.77 ± .02	190197	sw
70	525.27 ± .03	190378	-sw
71	521.97 ± .05	191582	sw
72	521.81 ± .05	191641	sw
73	521.54 ± .10	191740	da
74	518.88 ± .10	192723	sa
75	517.24 ± .10	193334	da
76	514.42 ± .10	194394	da
77	513.86 ± .10	194606	da
78	513.27 ± .10	194829	da
79	512.32 ± .05	195191	sa
80	510.46 ± .05	195902	sa
81	509.54 ± .03	196255	sa
82	509.27 ± .03	196359	sa
83	d 507.85 ± .10	196909	dw
84	506.69 ± .05	197359	sw
85	506.36 ± .05	197488	+sw
86	505.89 ± .10	197671	sa
87	505.42 ± .03	197855	—sx
88	504.40 ± .05	198255	—sx
89	503.64 ± .05	198555	—SX
90	502.87 ± .05	198859	—sx
91	502.13 ± .03	199152	—sw
92	501.74 ± .05	199306	sw
93	501.39 ± .05	199446	sw
94	500.37 ± .05	199852	—sw
95	499.74 ± .03	200104	—sw
96	498.54 ± .03	200586	sa
97	497.33 ± .05	201074	sw
98	497.06 ± .05	201183	+sx
99	496.11 ± .05	201568	da
100	495.69 ± .10	201739	sa
101	495.42 ± .05	201849	sw
102	495.15 ± .05	201959	sw
103	495.02 ± .05	202012	sa
104	494.39 ± .05	202269	-sw
105	493.80 ± .05	20251J	-sa
106	493.42 ± .05	202667	-sa
107	492.91 ± .03	202877	sa
108	492.10 ± .2	203210	dda
109	491.22 ± .03	203575	-sw
110	490.20 ± .05	203998	-sx
111	489.93 ± .05	204111	sa
112	489.66 ± .03	204223	sa
113	489.19 ± .03	204420	da
114	488.91 ± .03	204537	sa
115	488.59 ± .03	204671	+sa
116	488.23 ± .03	204821	+sa
117	487.93 ± .03	204947	sa
118	487.79 ± .03	205006	sw
119	487.68 ± .03	20S0S2	sw
120	487.03 ± .05	205326	sw
121	486.71 ± .05	205461	sw
122	485.55 ± .03	205952	+sw
123	485.25 ± .05	206079	-sw
124	483.12 ± .05	206988	+sa
125	482.20 ± .05	207383	sa
126	481.28 ± .05	207779	sw
127	480.47 ± .05	208130	-sa
128	478.93 ± .10	208799	da
129	478.30 ± .05	209074	da
130	477.51 ± .05	209420	da
131	477.12 ± .05	209591	sw
132	476.77 ± .05	209745	sw
133	476.00 ± .3	210080	dda
134	475.19 ± .05	210442	sw
135	*474.36 ± .05	210810	da
136	*473.42 ± .05	211229	da
137	*472.83 ± .05	211492	sa
138	*472.36 ± .05	211703	sa
139	*472.01 ± .05	211860	sa
140	*471.67 ± .05	212013	sa
141	*470.46 ± .05	212558	sa
142	*469.40 ± .05	21305	sa
143	*468.67 ± .05	213370	sa
144	*468.15 ± .05	213607	sa
145	467.72 ± .05	213803	sa
146	467.54 ± .05	213885	sa
147	467.02 ± .05	214124	da
148	466.30 ± .2	214450	da
149	465.80 ± .05	214684	sa
150	465.10 ± .05	215008	da
151	464.35 ± .05	215355	sa
152	463.27 ± .07	215857	sa
153	462.63 ± .07	216155	sa
154	462.23 ± .07	216343	sa
155	*461.00 ± .05	216920	+sa
156	460.31 ± .10	217245	dda
157	*459.68 ± .05	217543	sa
158	459.23 ± .05	217756	da
159	*458.63 ± .05	218041	sa
160	*458.04 ± .05	218322	sa
161	456.80 ± .2	218910	da
162	456.71 ± .07	218957	—sa
163	456.42 ± .05	219096	—sa
164	455.83 ± .05	219380	sa
165	455.40 ± .05	219587	sa
166	454.95 ± .05	219804	—sa
167	*454.34 ± .05	220099	—sa
168	454.00 ± .05	220264	sa
169	453.70 ± .05	220410	sa
170	*453.42 ± .05	220546	—sa
171	453.11 ± .07	220697	sa
172	452.70 ± .07	220897	-sx
173	*452.35 ± .10	221068	dda
174	452.06 ± .07	221210	sa
175	450.33 ± .05	222059	-da
176	449.67 ± .05	222385	da
177	449.15 ± .05	222643	da
178	448.42 ± .05	223005	da
179	448.01 ± .05	223209	sa
180	447.61 ± .05	223409	da
181	445.91 ± .05	224260	sa
182	*445.61 ± .05	224411	da
183	445.41 ± .05	224512	da
184	444.93 ± .05	224754	sa
185	444.38 ± .05	225033	sa
186	*443.73 ± .07	225362	da
187	443.27 ± .05	225596	da
188	442.91 ± .05	225779	da
189	*442.41 ± .07	226035	da
190	*441.46 ± .10	226521	sa
191	*441.01 ± .07	226752	sa
192	*440.59 ± .07	226968	sa
193	*440.33 ± .07	227102	sa
194	439.92 ± .07	227314	da
195	439.30 ± .07	227635	da
196	438.29 ± .07	228159	sa
197	437.64 ± .07	228498	sa
198	437.22 ± .05	228718	sa
199	436.82 ± .05	228927	sa
200	436.60 ± .05	229043	sa
201	436.15 ± .05	229279	+da
202	435.75 ± .05	229489	da
203	435.16 ± .05	229801	sa
204	*434.34 ± .05	230234	da
205	*433.30 ± .05	230787	da
206	*432.31 ± .05	231315	da
207	431.87 ± .05	231551	sa
208	*431.55 ± .05	231723	sa
209	*431.26 ± .05	231879	sa
210	*430.90 ± .05	232072	sa
211	*430.63 ± .05	232218	sa
212	*430.45 ± .05	232315	sa
213	*430.31 ± .05	232391	sa
214	429.67 ± .05	232737	+sa
215	428.36 ± .05	233448	sa
216	428.14 ± .05	233568	sa
217	427.92 ± .05	233689	sa
218	426.61 ± .05	234406	+sa
219	425.88 ± .05	234808	da
220	425.51 ± .05	235012	da
221	424.97 ± .05	235311	sa
222	424.47 ± .10	235588	da
223	424.02 ± .10	235838	da
224	423.43 ± .10	236167	da
225	422.73 ± .10	236558	da
226	420.40 ± .2	237870	dda
227	418.00 ± .2	239230	dda
228	413.70 ± .10	241721	da
229	41O.30 ± .10	243724	da
230	408.94 ± .10	244535	sa
231	408.50 ± .10	244798	sa
232	407.67 ± .10	245296	sa
233	406.32 ± .10	246111	sa
234	406.07 ± .10	246263	sa
235	404.96 ± .10	246938	sa
236	404.63 ± .10	247139	sa
237	403.87 ± .10	247604	sa
238	401.90 ± .2	248820	da
239	401.24 ± .10	249227	sa
240	400.90 ± .10	249439	sa
241	399.94 ± .10	250038	da
242	399.56 ± .10	250275	da
243	399.00 ± .2	250630	da
244	397.72 ± .15	251433	da
245	396.70 ± .2	252080	da
246	395.66 ± .15	252742	da
247	392.28 ± .15	254920	dda
248	387.39 ± .15	258138	da
249	385.62 ± .15	259323	da
250	384.56 ± .15	260037	da
251	383.33 ± .15	260872	da
252	377.20 ± .15	265111	da
253	375.34 ± .15	266425	da

^aSign plus (+) or minus (−) represents the sign of q in the Fano [12] representation of noninteracting resonances. The letters s, d, dd, give a very rough idea of the sharpness or diffuseness of lines on a photographic plate. Naturally, this apparent width varies with gas pressure. The letters x w, or a indicate specifically if the resonance has been measured at (x) the point of highest rate of change of plate density (w) the point of maximum plate density, or (a) the point of minimum plate density (maximum absorption); e.g., sw, means a sharp resonance of low unknown (q) measured at the peak transmission point.

^bErrors shown represent the estimated absolute uncertainty. In the case of Xe the relative accuracies are of the order of 0.02 Å better than the estimated absolute uncertainty.

^cResonances denoted by an asterisk (*) are listed in table 4 as possible members of Rydberg series.

^dPossible double resonance.

The absorption cross section in the region of a resonance can be parameterized in the form:

$$\sigma (E)={\sigma }_a\frac{{(q+\in )}^2}{\mathrm{l}+{\in }^2}+{\sigma }_b$$

with $\in =(E-E_r)/\frac{1}{2}\text{Γ}$, where the quantities E and E_r are the photon energy and the resonance energy (ϵ = 0), respectively. The parameter q is the resonance profile index and is defined in terms of transition matrix elements between the ground state, the modified discrete state and the continuum states. The half-width of the resonance is Γ, the quantity σ_a is the cross section associated with the fraction of the available continua with which the discrete state interacts, and σ_b is the cross section associated with the fraction of the continua which does not enter into the interaction. The parameter ρ, called the correlation index [12], is obtained from the relation $p^2=\frac{{\sigma }_a}{{\sigma }_a+{\sigma }_b}$.

Experimentally, when q is positive, a region of low absorption at low energy immediately precedes a region of increased absorption at higher energy. For a negative q, the reverse is true. If q is of the order of 1, the resonance appears quite asymmetric. If q is large and ρ² is small, the resonance looks like a conventional Lorentz absorption profile (absorption-type resonance), but if q is close to zero, the resonance has only a reduced-absorption zone (window-type resonance). When possible, in tables 1 and 2 the sign q is given. Where the letter x, a, and w are used, the resonance appears to be an asymmetric, absorption or window-type resonance, respectively, and has been measured as such.

3.1. One-Electron Transitions

The most prominent series should be those associated with one-electron transitions. This was found to be the case in Ne and Ar, and is equally true in Kr and Xe. The ground state of the noble gases is a ¹S₀. In a photoexcitation process, therefore, the upper state involved must have J = 1, regardless of the coupling conditions.

Since strict L–S coupling is not applicable, the strongest Rydberg series would be due to transitions:

$$\mathrm{K}\mathrm{r}:\mathrm{\hspace{0.17em}}4s^{2}4p^{61}{\mathrm{S}}_0\to 4s4p^6{(}^2{\mathrm{S}}_{1/2})np;n=5,\mathrm{6..}(\mathrm{two}J=1\mathrm{components})$$

$$\mathrm{X}\mathrm{e}:\mathrm{\hspace{0.17em}}5s^{2}5p^{61}{\mathrm{S}}_0\to 5\mathrm{s}5p^6{(}^2{S}_{1/2})np;n=6,\mathrm{7..}(\mathrm{two}J=1\mathrm{components})$$

The upper configurations have only two J = 1 states, and transitions to upper states of other J cannot occur due to the rigorous selection rules: ΔJ = 0, ±1; 0 ⇸ 0.

Thus we might expect to resolve at low n values, the two J = 1 members converging to the known ²S_1/2 limits of Kr ii or Xe ii. (This limit occurs in Kr at 450.62 Å and in Xe at 529.91 Å).

In the case of Kr, we see three “strong” window resonances in the region where the first members of the one-electron excitation series should occur. In Xe, one “strong” resonance and three somewhat weaker resonances are observed. “Strong” in this case means high visibility rather than a large oscillator strength, since the visibility of resonances depends also on the interference effects. Additionally, the ability to see window resonances is photographically enhanced at lower pressures.

The choice of the two J = 1 components of the first member of the Rydberg series is by no means unambiguous. The two components chosen in Kr are seen in the top photograph of figure 1 and again in the densitometer trace, figure 2. The resonances are denoted by their code numbers 3 and 5, see table 1. The wavelengths, principal quantum numbers (n) and effective quantum numbers (n*) are given in table 3, part A. Recent work appears to support the above choice. Reader et al. [13] noted that the effective quantum number of the 5p electron in the 4s4p⁶5p state in the isoelectronic sequence Zr v, Nb vi, and Mo vii consistently differed from the n* in the 4s²4p⁶5p state of Nb v, Mo vi, and Tc vii by 0.040. Extrapolating this relationship the n* for the 4s4p⁶5p state of Kr i can be obtained from the n* for the 4s²4p⁶5p state of Rb i (2.289). The result, 2.329, is in good agreement with the value of 2.323 for the assigned resonance to this state in table 3.

Figure 2. A microdensitometer trace of the absorption spectrum of Kr in the region 435–500 Å.

The main series of “window” resonances are indicated by vertical lines. Note the two J = 1 components for the n = 5 and 6 members. The code numbers alongside the resonances allow determination of their wavelengths (and in some cases classification) via tables 1 and 3.

Table 3. Resonances in Kr i grouped as members of possible series converging to the limits indicated.

The principal quantum number (n), and effective quantum number (n*) associated with the appropriate series limits are given. The levels in Kr ii to which these series converge are arranged in order of increasing energy. Their positions are obtained from data [18] on the Kr ii, added to 112915 cm⁻¹, the first ionization energy of Kr i.

Code number	λ(Å)	n	n*
(A) Limit: −4s4p6(2S1/2) = 221915 cm−1; Series: −4s4p6np
5	496.07	5	2.323
11	471.23	6	3.363
14	462.71	7	4.351
18	458.69	8	5.303
22	456.12	9	6.406
24	454.73	10	7.399
26	453.73	11	8.498
27	453.15	12	9.42
28	452.68	13	10.43
29	452.34	14	11.41
30	452.07	15	12.43
32	451.86	16	13.44
33	451.69	17	14.47
34	451.56	18	15.44
35	451.45	19	16.43
Second series of two available, having J = 1 final state
3	497.50	5	2.304
10	471.48	6	3.343
(B) Unknown limita = 240300 cm−1
63	417.96	13	10.26a (9.35)
64	417.62	14	11.38 (10.18)
65	417.39	15	12.38 (10.88)
66	417.22	16	13.32 (11.49)
(C): −4p4(1S)5s(2S1/2) = 258727 cm−1; Series: −4p45snp
86	391.44	8	5.59
87	390.49	9	6.45
89	389.48	10	7.46
90	388.84	11	8.41
91	388.37	12	9.41
92	388.05	13	10.33
93	387.79	14	11.33
94	387.60	15	12.27
96	387.08	16	13.21
(D) Limit: −4p4(1D)4d(2D5/2) = 262429 cm−1; Series: −4p44dnp
99	385.03	9	6.37
101	384.03	10	7.35
(E) Limit:−4p4(1D)4d(2P1/2) = 265100 cm−1: Series:−4p4dnp
112	378.97	12	9.46
113	378.65	13	16.46
114	378.43	14	11.36
115	378.23	15	12.43
(F) Limit:−4p4(1D)4d(2S1/2) = 273710 cm−1; Series:−4p44dnp
123	370.87	8	5.19
125	369.13	9	6.26
127	368.14	10	7.27
128	367.56	11	8.17
129	367.03	12	9.36
130	366.70	13	10.44
131	366.49	14	11.35
(G) Limit:−4p4(1S)4d(2D5/2) = 273927 cm−1; Series:−4p44dnp
124	370.13	8	5.41
126	368.60	9	6.46

^aThe nearest known limit [18] is (¹D)5s(²D_3/2) at 240512 cm⁻¹. One could assume this limit to be the apppropriate one, giving the values of n* shown in parentheses. Noninteger difference in n* through the series could possibly be explained by configuration interaction effects.

^bThis limit was previously assigned [19] to 4p⁴(³P)5d(⁴P_1/2). It was recently reassigned [18] by Minnhagen.

In Xe, the most prominent member of the quartet of resonances (Code Nos. 1, 2, 3, 4) has been chosen as the first member of the one-electron excitation series: 3, 16, 28 etc. This series can be seen in the lower photograph of figure 1 and also in the densitometer trace figure 3. The wavelengths and effective quantum numbers are given in table 4, part A. A choice has not been made for the second J = 1 component in Xe, although it is likely to be resonance 1 or 2.

Figure 3. A microdensitometer trace of the absorption spectrum of Xe in the region 525–600 Å.

The main series of “window” resonances is denoted by vertical lines. The code numbers allow determination of wavelengths (and in some cases classification) via tables 2 and 4. The absorption feature labeled X, is the third order of an absorption line [4] at 190.41 Å.

Table 4. Resonances in Xe i grouped as members of possible series converging to the limits indicated.

The principal quantum number (n) and effective quantum number (n*) associated with the appropriate series limits are given. The levels in Xe ii to which these series converge are obtained by adding 97834 cm⁻¹, the lowest ionization energy of Xe i, to terms [19] of Xe ii.

Code number	λ(Å)	n	n*
(A) Limit: −5s5p6(2S1/2) = 188708 cm−1; Series: −5s5p6np
3	591.77	6	2.359
16	557.83	7	3.409
28	546.08	8	4.433
a 37	540.54	9	5.440
40	537.46	10	6.438
45	535.55	11	7.437
48	534.27	12	8.450
b 49	533.34	13	9.52
51	532.76	14	10.44
55	531.21	19	15.47
57	530.93	21	17.48
58	530.83	22	18.41
59	530.74	23	19.39
(B) Limit: −5p4(3P)6s(4P5/2) = 190902 cm−1; Series: −5p−46snp
22	550.76	7	3.429
38	539.33	8	4.472
47	534.58	9	5.346
54	531.37	10	6.364
62	529.34	11	7.431
65	528.05	12	8.480
(C) Limit: −5p4(3P)6s(4P3/2) = 192898 cm−1: Series: −5p46snp
31	544.18	7	3.466
b 49	533.34	8	4.508
64	528.42	9	5.480
69	525.77	10	6.374
(D) Unknown Limitc = 212665 cm−1
135	474.36	8	7.691
136	473.42	9	8.742
137	472.83	10	9.68
138	472.36	11	10.68
139	472.01	12	11.68
140	471.67	13	12.97
(E) Limit: −5p4(3P)6p(4D3/2) = 214617 cm−1: Series: −5p46pndd
141	470.46	10	7.30
142	469.40	11	8.34
143	468.67	12	9.38
144	468.15	13	10.42
(F) Limit: −5p4(3P)6p(4S3/2) = 219463 cm−1; Series: −5p46pnd
155	461.00	9	6.57
157	459.68	10	7.56
159	458.63	11	8.78
160	458.04	12	9.80
(G) Limit: −5p4(1S)5d(2Dl/2) = 222136 cm−1; Series: −5p45dnp
167	454.34	11	7.34
170	453.42	12	8.31
173	452.35	13	9.41
(H) Limit: −5p4(1D)6p(2F7/2) = 227898cm−1; Series: −5p46pnd
182	445.61	8	5.61
186	443.73	9	6.58
189	442.41	10	7.67
190	441.46	11	8.93
191	441.01	12	9.79
192	440.59	13	10.87
193	440.33	14	11.74
(I) Limit: −5p4(3P)7s(4Pl/2) = 232895 cm−1; Series: −5p47snp
204	434.34	10	6.42
205	433.30	11	7.22
206	432.31	12	8.34
208	431.55	13	9.68
209	431.26	14	10.39
210	430.90	15	11.55
211	430.63	16	12.73
212	430.45	17	13.76
213	430.31	18	14.75

^aThe resonance at 540.62 Å is an alternative choice for the n = 9 member.

^bThis resonance appears to be double and is used in series (A) and (C).

^cThe nearest Xe ii levels are 5p⁴(¹D)5d(²F_5/2, _7/2) at 212585 cm⁻¹ and 212748 cm⁻¹, either of which would allow an nf series.

^dThe quantum defects for this series are more appropriate to a running p electron. However, assuming a correct assignment for the level in Xe ii, parity considerations require a running d electron (or an s electron).

Recent work [13] suggests that the main J = 1 component in Xe should have an effective quantum number n* = 2.391. If resoance 4 is taken as the first member of the series, its effective quantum number is 2.398. Resonance 3 chosen here gives n* = 2.359. This choice was made upon the basis of the great similarity in resonance profiles of line 3 and the following members of the series, resonances 16 and 28. Figure 3 clearly shows that line 3 is asymmetric, with a low positive q, whereas resonance 4 has a q of the opposite sign. In fact, Ederer [10] has shown that the values of q and ρ² for resonance 3 are 0.23(±.04) and 0.65(±.03), for resonance 4 are −0.14(±.04) and 0.50(±.04) and for resonance 16 are 0.16(±.04) and 0.67(±.02). In addition, we can compare the equivalent one-electron excitation states in Ne, Ar, Kr, and Xe and the way in which the first member of the Rydberg series is always depressed (moved to longer wavelengths) relative to a simple theoretical estimate of its location, due to screening effects. The increase in this screening effect from Ne through Kr leads us to expect the strongest J = 1 component in Xe to lie almost exactly where it is. Nevertheless, it is conceivable that configuration interaction may cause resonances to interchange intensities, and affect their shapes. Good theoretical calculations will be required to resolve this situation.

If we move to higher series members in Kr, we find that resonance 18 has an unusually low effective quantum number and a low intensity (see fig. 2). On the basis of the quantum defect alone, resonance 18, the n= 8 member of this series, was chosen as a member of the Rydberg series. Clearly, resonance 19 is much “stronger” (see also Ederer [10]) and was observed by Samson [15] and classified as a member of the series with n* = 5.593. Once again, there is ambiguity. The remainder of the series is quite definitely established on a basis of quantum defects, intensities and profiles.

In tracing the development of the Xe series, we find the n = 9 member to be double and an arbitrary choice must be made from resonances 36 and 37. Other workers [14, 15] did not resolve these resonances. Configuration interactions cause members n = 15 through 18 and n = 20 to be missing.

Finally, in table 5, we see a comparison of the long wavelength resonances in Kr and Xe with other workers. In Kr, the present data is compared with the photoabsorption work of Samson [14, 15] and the electron spectroscopic observations of Siegbahn and co-workers [16]. In Xe, comparison is also made with the photoabsorption work of Mansfield [17] (Mansfield measured Kr also, and was in agreement with the present work for the stronger transitions). The error limits quoted by Samson are ±0.05 Å, those of Siegbahn et al. are of the order of 0.2 Å. Mansfield gave no estimated error, but he had some calibration problems in the region of 585–600 Å due to lack of standards. The accuracy of the present measurements is also impaired in this region of the spectrum because of slight instrumental errors and this is reflected in the somewhat increased error limits given to the resonances in that region. Almost all of the wavelengths of Samson agree, within the combined error limits, with the present data, even in the range 585–600 Å.

Table 5. A comparison of the wavelengths of some of the resonances measured in the present work and those of other workers.

The Siegbahn [16] wavelengths are obtained using the conversion factor λ = 12398/E(eV).

Krypton				Xenon
Code	Present work	Samson [15]	Siegbahn [16]	Code	Present work	Samson [l5]	Mansfield [17]	Siegbahn [16]
1	501.23	501.14		1	599.99	599.95	599.81
3	497.50	497.44	497.1	2	595.93	595.92	595.83
4	496.90	496.85		3	591.77	591.81	591.67	592.1
5	496.07	496.00	495.7	4	589.54	589.62	589.50	589.5
10	471.48	471.55	471.2	5	586.29		586.24
14	462.71	462.69	462.8	6	582.74		582.72
18	458.69		458.8	7	581.11		581.07
19	a 457.86	457.85		8	579.98		579.94
22	456.12	456.10	456.0	9	579.16	14 579.25	579.15
24	454.73	454.71	455.0	10	570.79	14 570.90	570.80
26	453.73	453.71	453.8	15	558.78		558.78
27	453.14	453.14		16	557.83	557.92	557.86	557.7
29	452.32	452.32		19	555.28		555.32
30	452.07	452.01		21	552.00	14 552.07	552.02
32	451.86	451.85		22	550.76		550.77
				28	546.08	546.16		546.2
				b 36	540.62	540.71		540.5
				37	540.54
				40	537.46	537.40
				45	535.55	535.62

^aResonance 18 was chosen in the present work, on the basis of quantum defect; for 4s4p⁶8p. However, resonance 19 is a considerably stronger line seen also by Samson and assigned to the 8p state.

^bTwo resonances, equally strong, just resolved.

The data of Siegbahn et al. was obtained by firing electrons of an energy of several keV into the noble gases, and measuring the energies (typically 8 to 14 eV) of the electrons released in the subsequent autoionization process, with a spherical electrostatic analyzer. Rydberg series of electron lines were found corresponding to transitions from excited states of neutral atoms to the ground state of the ions. By measuring the kinetic energy of electrons produced in the autoionization process:

$$4s4p^{6}np\to 4s^{2}4p^5{(}^2{\text{P}}_{1/2,3/2})+e$$

and knowing the energy of the 4s²4p⁵(²P_{1/2, 3/2}) states of Kr ii, they were able to calculate the energy of the excited state before autoionization. Since the Siegbahn data was normalized to the present data at certain wavelengths, it cannot be thought of as independent. It is interesting, however, to note that these workers picked out a second J = 1 component for the 4s4p⁶5p state of Kr. Even though the absolute wavelengths of resonances 3 and 5 disagree by 0.3 Å, the difference in wavelengths of 1.4 Å is in agreement with the present data. In Xe, however, the implication might be that resonances 3 and 4 are the two J = 1 components, in agreement with another recent estimate [13], and in disagreement with the present classification. It should be pointed out, however, that excitation by electron bombardment can excite, in general, many transitions not allowed optically and that often such nonoptically allowed transitions are preferred. In addition, the resonance profiles may be completely different.

3.2. Two-Electron Transitions

It has been pointed out that only two J = 1 components can be expected for states such as 4s4p⁶5p in Kr.

The remaining resonances in Kr, such as 1, 2, 4, 6, 7, 8 etc. (see fig. 2) must therefore be classified, from energy considerations, in terms of two-electron transitions, viz:

$$\begin{array}{l}\text{K}\mathrm{r}:\mathrm{\hspace{0.17em}}4s^{2}4p^{61}{S}_0\to 4s^{2}4p^4{(}^3\text{P,}{}^1\text{D,}{}^1\mathrm{S)}nln\text{'}l\text{'}andin\\ \text{X}\mathrm{e}:\mathrm{\hspace{0.17em}}5s^{2}5p^{61}{S}_0\to 5s5p^4{(}^3\text{P,}{}^1\text{D,}{}^1\mathrm{S)}\mathrm{\hspace{0.17em}}nln\text{'}l\text{'}\end{array}$$

Here ll′ = sp, sf, pd, pf.

The term possibilities are just those outlined previously in Ar [3]. As shown, the grandparent term may be ³P, ¹D, or ¹S. Taking the simplest case of 5s5p in Kr, the number of possible J = 1 components is 14, with 3 of these being ¹P₁, in strict L–S coupling. We know, however, that L–S coupling does not prevail, and we may expect a large number of excited states with J = 1. Experimentally, one observes few of this potentially large number of resonances.

As in Ar, we can make crude estimates of the expected positions of resonances from the known levels of the ion [18, 19] and typical quantum defects for the s, p, d, and f electrons. Because the spectra observed are quite rich and because of screening and configuration interaction effects, such estimates cannot be sufficiently accurate to establish definite assignments.

In the cases of Ne and Ar a number of low-lying two-electron excitation states were identified. In Kr and Xe virtually none have been assigned. In the absence of good calculations, we can only identify series with high-lying members. Intensity sharing interactions appear to be responsible for the fact that we see any series at all.

In both Kr and Xe, quantum defects have been calculated for all the resonances to the available [18, 19] known limits. As a result of this analysis, only 28 resonances in Kr and 43 in Xe have been grouped into probable Rydberg series. In the Ar case, one experimental fact was very obvious – that of all the possible excited configurations, those of the type: – 3p⁴3dnl and 3p⁴4snl dominated the spectrum. Series such as 3p⁴4pns were hardly in evidence. This tendency is equally pronounced in Kr, where all of the series are of the type 4p⁴5snp or 4p⁴4dnp.

Turning to table 3 (B), the unidentified series having a limit at 240300 cm⁻¹ may be due to transitions to states (¹D)5s(²D_3/2)np. However, using Minnhagen’s value for this limit [18], we must then invoke certain configuration interaction effects to explain the unusual run of effective quantum numbers (inside the brackets).

In Xe, if the present tentative assignments are correct, the emphasis on running electrons of odd parity is no longer evident. Indeed, there are apparently two series of the type 5p⁴6pnd. Another series is tentatively labelled 6pnd (table 4 (E)) but the defects are more appropriate for a running p electron – forbidden on the grounds of nonconservation of parity if the state in Xe ii has been correctly identified [19].

Also in table 4, the series (D) with an unidentified limit, may well be associated with a series of the type 5p⁴5dnf.

Some of the more obvious series in Kr and Xe are indicated by lines above and below the spectra of figure 1. In Kr we can see the series A, B, C, F and G of table 3; in Xe we see the series A, B, D and I of table 4.

4. Conclusions

The one- and two-electron excitation resonances listed into the series above represent only one quarter of those observed. The basic problem is one of unfolding the complicated configuration interactions present, which displace levels from the locations expected on simple theoretical grounds, and produce intensity anomalies. Even within a single series, the profiles of the resonances may change with increasing principal quantum number. In others, only high series members are evident. It appears that a substantial theoretical effort will be required to analyze the spectra further, even in those regions where relatively few resonances occur. Original prints of the spectra shown in figure 1 can be made available to those interested in furthering the interpretation.