Monte Carlo estimation of average energy required to produce an ion pair in noble gases by electrons with energies from 1 keV to 100 MeV

Figures & data

Table 1. Electron creation statistics when 10,000 electrons with energy 1 MeV are stopped in xenon.

	Above electron energy cut-off (10.96 eV)
	Number of events N		Energy per source el. (MeV)		All electrons (MCNelectron)
Type	MCNelectron	MCNP6	MCNelectron	MCNP6	N	E (MeV)
Compton recoil	602	595	5.2155E−03	5.5348E−03	>602^a	5.2197E−03
Photo-electric	32,292	32,150	3.5510E−02	3.5826E−02	34,871	3.5511E−02
Photon Auger	160,344	161,032	4.7611E−03	4.7766E−03	166,204	4.7666E−03
Electron Auger	42,328,725	42,144,673	2.7419E−01	2.7305E−01	43,161,928	2.7500E−01
Knock-on	54,395,730	54,147,437	6.8568E−01	6.8600E−01	266,798,312	7.3475E−01
Total^b	96,917,693	96,485,887	1.0054E+00	1.0052E+00	310,161,917	1.0552E+00

^aIf the target is infinite in all directions, MCNelectron stops counting photon collisions when incoherent scattering is the only remaining energy-loss process and photon energy is less than a certain threshold value. Then the value of E is increased, but N is not changed.

^bThe statistics do not take into account creation of 10,000 source electrons with energy 1 MeV.

Table 2. Electron loss statistics when 10,000 electrons with energy 1 MeV are stopped in xenon.

	Number of events		Average energy loss per source electron (MeV)
Type	MCNelectron	MCNP6	MCNelectron	MCNP6
Energy cut-off	96,927,693	96,495,887	5.3490E−02	5.3322E−02
Bremsstrahlung	45,691	N/A	3.9985E−02	4.0617E−02
Excitation	350,278,422	N/A	4.9860E−01	5.0220E−01
Electroionization	266,798,312	N/A	1.4133E+00	1.4091E+00
Total^a	96,927,693	96,495,887	2.0054E+00	2.0052E+00

^aIn order to facilitate comparison with MCNP6, the total number of events for MCNelectron includes only events when the electron energy dropped below the cut-off energy (10.96 eV).

Table 3. Photon creation statistics when 10,000 electrons with energy 1 MeV are stopped in xenon.

	Number of events		Average energy per source electron (MeV)
Type	MCNelectron	MCNP6	MCNelectron	MCNP6
Bremsstrahlung	32,953	33,494	3.9984E−02	4.0616E−02
Electron X-rays	12,399	12,070	5.7299E−03	5.7438E−03
Compton fluorescence	29	25	5.0537E−05	5.1409E−05
First fluorescence	2234	2318	5.7253E−03	6.0018E−03
Second fluorescence	395	375	1.4507E−04	1.3483E−04
Total	48,010	48,282	5.1635E−02	5.2548E−02

Table 4. Photon loss statistics when 10,000 electrons with energy 1 MeV are stopped in xenon.

	Number of events		Energy loss per source electron (MeV)
Type	MCNelectron	MCNP6	MCNelectron	MCNP6
Energy cut-off	13,139	13,535	1.3139E−06	1.3535E−06
Compton scattering	602	N/A	5.2197E−03	5.5391E−03
Capture	34,871	34,747	4.6414E−02	4.7008E−02
Total^a	48,010	48,282	5.1635E−02	5.2548E−02

^aIn order to facilitate comparison with MCNP6, the total number of events for MCNelectron does not include Compton scattering events.

Figure 1. Probability density functions (a) and corresponding cumulative distribution functions (b) of knock-on electrons in neon for two values of the incident electron energy.

Figure 2. Probability density functions (a) and corresponding cumulative distribution functions (b) of knock-on electrons in xenon for two values of the incident electron energy.

Table 5. Average values of the ratio of excitation and ionization cross sections in the energy range from 40 to 200 eV.

Data-set	He	Ne	Ar	Kr	Xe
ENDF/B-VI.8	0.65	0.026	0.90	1.15	2.4
BIAGI-v8.9	0.50	0.30	0.27	0.27	0.36
SIGLO	0.35	0.28	0.29	0.30	0.36

Figure 3. Energy dependence of (a) electroionization and (b) excitation cross section for electrons in neon.

Figure 4. Energy dependence of (a) electroionization and (b) excitation cross section for electrons in xenon.

Figure 5. Comparison of calculated values of W for neon: (a) using BIAGI-v8.9 data and (b) using SIGLO data.

Figure 6. Comparison of calculated values of W for xenon: (a) using BIAGI-v8.9 data and (b) using SIGLO data.

Table 6. Average experimental and calculated values of W (eV) and their standard deviations.

	He		Ne		Ar		Kr		Xe
Data-set	Avg	SD	Avg	SD	Avg	SD	Avg	SD	Avg	SD
Experiment	41.3	1.0	35.4	0.9	26.4	0.5	24.4	0.5	22.1	0.4
ENDF/B-VI.8	44.3	1.7	27.31	0.10	29.1	1.2	29.5	1.2	33.4	1.7
BIAGI-v8.9
No interpolation	46.4	1.1	37.95	0.73	26.32	0.81	25.16	0.90	25.6	1.5
Exc. 100 keV, ion. 100 keV	45.98	0.88	38.36	0.77	25.50	0.37	23.79	0.12	23.51	0.88
Exc. 500 keV, ion. 100 keV	45.81	0.86	38.47	0.76	25.36	0.30	23.66	0.04	23.05	0.63
Average (with interp.)	45.90	0.87	38.42	0.77	25.43	0.35	23.72	0.09	23.28	0.75
SIGLO
No interpolation	43.73	0.85	37.39	0.58	26.07	0.42	27.99	1.21	25.8	1.7
Exc. 100 keV, ion. 100 keV	42.27	0.63	37.57	0.54	25.99	0.36	24.17	0.14	23.3	1.0
Exc. 500 keV, ion. 100 keV	41.76	0.68	37.66	0.52	25.97	0.34	23.83	0.02	22.79	0.73
Average (with interp.)	42.02	0.66	37.62	0.53	25.98	0.35	24.00	0.10	23.04	0.87