Neutron-induced background in the CONUS experiment

TL;DR

The paper investigates neutron-induced backgrounds in the CONUS neutrino detection experiment, demonstrating that the reactor-correlated neutron field can be effectively mitigated using shielding, enabling neutrino detection with minimal background interference.

Contribution

It provides a detailed measurement and simulation-based analysis of neutron backgrounds at the CONUS experiment site, showing effective shielding of reactor-induced neutrons.

Findings

Reactor-induced neutron background is significantly reduced by shielding.

Neutron background is below the expected neutrino signal by at least one order of magnitude.

Thermal power correlated neutron field can be mitigated effectively.

Abstract

CONUS is a novel experiment aiming at detecting elastic neutrino nucleus scattering in the fully coherent regime using high-purity Germanium (Ge) detectors and a reactor as antineutrino ($\bar\nu$) source. The detector setup is installed at the commercial nuclear power plant in Brokdorf, Germany, at a very small distance to the reactor core in order to guarantee a high flux of more than 10$^{13}\bar\nu$/(s$\cdot$cm$^2$). For the experiment, a good understanding of neutron-induced background events is required, as the neutron recoil signals can mimic the predicted neutrino interactions. Especially neutron-induced events correlated with the thermal power generation are troublesome for CONUS. On-site measurements revealed the presence of a thermal power correlated, highly thermalized neutron field with a fluence rate of (745$\pm$30)cm$^{-2}$d$^{-1}$. These neutrons that are produced by nuclear fission inside the reactor core, are reduced by a factor of $\sim$10$^{20}$ on their way to the CONUS shield. With a high-purity Ge detector without shield the $\gamma$-ray background was examined including highly thermal power correlated $^{16}$N decay products as well as $\gamma$-lines from neutron capture. Using the measured neutron spectrum as input, it was shown, with the help of Monte Carlo simulations, that the thermal power correlated field is successfully mitigated by the installed CONUS shield. The reactor-induced background contribution in the region of interest is exceeded by the expected signal by at least one order of magnitude assuming a realistic ionization quenching factor of 0.2.

Tables

Table 1. Table 1: Contributions to the uncertainty of the thermal power P th estimation from the energy balance in the secondary circuit.

syst. uncertainty	rel. uncertainty
	on Pth(%)
temperature	0.54
flow meter	1.64
moisture	1.56

Table 2. Table 2: Activity of concrete samples from room A408 and the MPIK laboratory, determined by HPGe spectrometer screening measurements at the underground laboratory in Heidelberg. The standard values are mean values from the activities of concrete from several countries ordinaryconcrete (n.d.=no data).

isotope	KBR A408	MPIK lab	standard
	[Bq/kg]	[Bq/kg]	[Bq/kg]
238U	37	12$\pm$5	n.d.
226Ra	13.2$\pm$0.2	12.8$\pm$0.4	44$\pm$21
232Th	15.3$\pm$0.3	16.6$\pm$0.8	30$\pm$14
228Ra	14.9$\pm$0.3	17.2$\pm$0.8	n.d.
137Cs	1.37$\pm$0.07	<0.03	n.d.
60Co	0.2–1.5	<0.03	n.d.
40K	433$\pm$12	112$\pm$7	240$\pm$108

Table 3. Table 3: Geant4 MC models for neutron propagation and absorption.

interaction	model	energy range	cross section
elastic	hElasticCHIPS	19.5MeVE10 TeV	GheishaElastic, ChipsNeutronElasticXS
	NeutronHPElastic	20MeV	GheishaElastic, ChipsNeutronElasticXS, NeutronHPElasticXS
inelastic	BertiniCascade	19.9MeVE9.9 GeV	GheishaInelastic, Barashenkov-Glauber
	NeutronHPInelastic	20MeV	GheishaInelastic, Barashenkov-Glauber, NeutronHPInelasticXS
capture	G4LCapture	19.9MeVE2 TeV	GheishaCaptureXS
	NeutronHPCapture	20MeV	GheishaCaptureXS, NeutronHPCaptureXS
fission	G4LFission	19.9MeVE2 TeV	GheishaFissionXS
	NeutronHPFission	20MeV	GheishaFissionXS, NeutronHPFissionXS

Table 4. Table 4: The branching ratio (br) in Geant4 of the main γ 𝛾 \gamma -lines from neutron capture on the isotopes relevant at KBR are compared with literature values. For the lines marked with (*) the MC generates two neighbouring γ 𝛾 \gamma -lines close in energy. Out of those one was recognized to be not physical and was neglected. The absolute branching ratio refers to the ratio of emitted γ 𝛾 \gamma -rays per neutron capture (given for strongest line), while the relative branching ratio is given in respect to the strongest emitted line.

neutron capture	energy [keV] capgamdatabase	br MC	br lit
54Fe(n,$\gamma$)55Fe	9297.80$\pm$1.00	abs. 49.9(*)	abs. 56.8$\pm$4.9 EGAF
56Fe(n,$\gamma$)57Fe	7645.58$\pm$0.10	abs. 23.6	abs. 29.00$\pm$4.94 capgamdatabase
\hdashline	7631.18$\pm$0.10	rel. 86.22(*)	rel. 86.21$\pm$19.94 capgamdatabase
	7278.82$\pm$0.90	rel. 20.70	rel. 20.69$\pm$4.58 capgamdatabase
63Cu(n,$\gamma$)64Cu	7916.26$\pm$0.08	abs. 28.74(*)	abs. 33.10$\pm$0.60 capgamdatabase
\hdashline	7638.00$\pm$0.09	rel. 48.94	rel. 48.99$\pm$1.50 capgamdatabase
	7307.31$\pm$0.06	rel. 27.07	rel. 27.18$\pm$0.61 capgamdatabase
	7253.05$\pm$0.06	rel. 12.54	rel. 12.48$\pm$0.27 capgamdatabase

Table 5. Table 5: Overview of data sets collected during the measurement campaigns with the NEMUS spectrometer in room A408 at KBR.

data	reactor	time	Bonner spheres
set	state	period	arrangement
DS-1	ON	08.12.16–04.01.17	all spheres used
			simultaneously
DS-2	OFF	09.02.–26.02.17	all spheres used
			simultaneously
DS-3	ON	31.08.–04.10.17	spheres swapped
			at central position

Table 6. Table 6: Neutron fluence Φ ( 1 ) superscript 𝛷 1 \mathit{\Phi}^{(1)} derived from the analysis of the DS-3 measurement, and normalized to the KBR thermal energy output of 1 GW h. The uncertainties are stated as standard uncertainties (1 standard deviation). The E n subscript 𝐸 n E_{\text{n}} regions are defined as follows: thermal [ 1.0 × 10 − 9 ,  4.0 × 10 − 7 ] 1.0 superscript 10 9 4.0 superscript 10 7 [1.0\times 10^{-9},\,4.0\times 10^{-7}]  MeV; intermediate [ 4.0 × 10 − 7 ,  0.1 ] 4.0 superscript 10 7 0.1 [4.0\times 10^{-7},\,0.1]  MeV; fast [ 0.1 ,  19.6 ] 0.1 19.6 [0.1,\,19.6]  MeV.

$E_{\text{n}}$ region	${\Phi }^{\left(1\right)}$
	[${\text{cm}}^{-2}{\left(\text{GW\hspace{0.17em}h}\right)}^{-1}$]
thermal	$6.42\pm 0.41$
intermediate	$1.56\pm 0.21$
fast	$0.15\pm 0.05$
\hdashline total	$8.13\pm 0.32$

Table 7. Table 7: Neutron fluence rate Φ ( 2 ) superscript 𝛷 2 \mathit{\Phi}^{(2)} derived from the analysis of the DS-2 measurement (reactor OFF), normalized per 24 h. The uncertainties are stated as standard uncertainties (1 standard deviation). The definition of the E n subscript 𝐸 n E_{\text{n}} regions is identical to Table  5.2.1 .

$E_{\text{n}}$ region	${\Phi }^{\left(2\right)}$
	[${\text{cm}}^{-2}{\text{d}}^{-1}$]
thermal	$4.47\pm 0.67$
intermediate	$4.19\pm 1.15$
fast	$6.35\pm 0.96$
\hdashline total	$15.03\pm 0.99$

Table 8. Table 8: Comparison of neutron fluence rates Φ mean ( 1 ) subscript superscript 𝛷 1 mean \mathit{\Phi}^{(1)}_{\text{mean}} (reactor ON at constant mean level for time duration of 24 h) and Φ ( 2 ) superscript 𝛷 2 \mathit{\Phi}^{(2)} (reactor OFF), and their difference Φ mean (res) subscript superscript 𝛷 (res) mean \mathit{\Phi}^{\text{(res)}}_{\text{mean}} . All quantities are stated in units of [ cm − 2 ​  d − 1 superscript cm 2 superscript  d 1 \text{cm}^{-2}\,\text{\,d}^{-1} ]. The uncertainties are stated as standard uncertainties (1 standard deviation). The definition of the E n subscript 𝐸 n E_{\text{n}} regions is identical to the one used in Table  5.2.1 .

$E_{\text{n}}$ region	${\Phi }_{\text{mean}}^{\left(1\right)}$	${\Phi }^{\left(2\right)}$	${\Phi }_{\text{mean}}^{\text{(res)}}$
thermal	$534.8\pm 34.4$	$4.47\pm 0.67$	$530.3\pm 34.4$
intermediate	$130.0\pm 17.2$	$4.19\pm 1.15$	$125.8\pm 17.3$
fast	$12.3\pm 4.1$	$6.35\pm 0.96$	$6.0\pm 4.2$
\hdashlinetotal	$677.2\pm 27.0$	$15.03\pm 0.99$	$662.2\pm 27.1$

Table 9. Table 9: Supression of neutron fluence rate during propagation from reactor core to A408 in the MC corresponding to the respective surfaces.

location	area [m2]	suppression factor to previous	maximum neutron energy
reactor core	42.2 (cylinder)	1	$>$20 MeV
inner wall of RPV (I)	62 (cylinder)	1.6$\cdot$10-4	16.2 MeV
outside wall biological shield (II)	355.2 (cylinder)	6.5$\cdot$10-6	2.5 MeV
outside wall A408 (III)	18.4 (3 plates)	9$\cdot$10-3	1 MeV
inside wall A408 (IV)	10.2 (3 plates)	4$\cdot$10-8	0.17 eV
total	1	3.6$\cdot$10-20

Table 10. Table 10: Reactor physics input for the calculation of the neutrons produced in the reactor core that is used for the normalization of the MC simulation.

fission isotope	energy release per fission [MeV] MCnorm:Ma2013	fission fraction An2016 ,Djurcic:2008ny	number of neutrons per fission MCnorm:Kopeikin2004
235U	202.36$\pm$0.26	56.8$\pm$3.2	2.432$\pm$0.004
239Pu	211.12$\pm$0.34	30.2$\pm$0.4	2.875$\pm$0.006
238U	205.99$\pm$0.52	7.6$\pm$2.4	2.937$\pm$0.007
241Pu	214.26$\pm$0.33	5.4$\pm$0.7	2.829$\pm$0.011

Table 11. Table 11: Identified thermal power correlated γ 𝛾 \gamma -lines in the spectrum of the non-shielded CONRAD detector inside A408 during reactor ON time. The energy and branching ratios (br) from literature are given as well. The count rates marked with * were measured as one-peak structure and the single count rates were extracted as described in the text. (1) and (2) mark the different ways the MC is scaled. For (1), the measured thermal neutron fluence inside A408 has been used ((597 ± plus-or-minus \pm 39) cm -2 d -1 for 3.9 GW) and thus the uncertainties of the BSS measurement result dominate the uncertainties. For (2), the MC has been scaled with the number of neutrons expected to arrive at the outside wall from the ab initio calculation starting at the reactor core ((477 ± plus-or-minus \pm 20) ⋅ ⋅ \cdot 10 6  d -1 for 3.9 GW). Here, only statistic uncertainties and uncertainties on the literature values are included.

energy [keVee]	energy lit [keV]	count rate [cts/d/GW]	count rate MC [cts/d/GW]
53Fe(n,$\gamma$)54Fe
8790.9$\pm$0.6	8786.8$\pm$1.0 SEP	9.6$\pm$0.6	(2)9$\pm$1
9301.0$\pm$0.6	9297.8$\pm$1.0 (br 100%)	11.3$\pm$0.5	(2)11$\pm$1
56Fe(n,$\gamma$)57Fe
7280.0$\pm$0.7	7278.82$\pm$0.09 (br 20.69%)	11.5$\pm$1.1	(2)13$\pm$1
7632.8$\pm$0.1	7631.2$\pm$0.1 (br 100%)	137$\pm$4*	(2)111$\pm$1
7646.6$\pm$0.1	7645.6$\pm$0.1 (br 86.21%)	double peak
63Cu(n,$\gamma$)64Cu
7406.2$\pm$0.3	7405.26$\pm$0.08 SEP	27.2$\pm$1.3	(1)37$\pm$3
n. d.	7638.00$\pm$0.09 (br 48.94%)	15.7$\pm$1.6*	(1)19$\pm$2
7916.9$\pm$0.2	7916.26$\pm$0.08 (br 100%)	29.7$\pm$1.0	(1)37$\pm$3
16O(n,p)16N
5106.96$\pm$0.01	5106.63$\pm$0.04 DEP	12612$\pm$146
5617.51$\pm$0.01	5617.63$\pm$0.04 SEP	49972$\pm$575
6093.28$\pm$0.04	6093.15$\pm$0.14 DEP	1605$\pm$21
6128.14$\pm$0.01	6128.63$\pm$0.04 (br 67.0%)	85086$\pm$979
6604.36$\pm$0.01	6604.15$\pm$0.14 SEP	7163$\pm$83
6915.0$\pm$0.4	6915.5$\pm$0.6 (br 0.038%)	155$\pm$4
7115.37$\pm$0.02	7115.15$\pm$0.14 (br 4.9%)	10097$\pm$116
7848.4$\pm$0.3	7847.3$\pm$0.5 DEP	31$\pm$1
8359.7$\pm$0.1	8358.3$\pm$0.5 SEP	135$\pm$2
8870.8$\pm$0.1	8869.3$\pm$0.5 (br 0.076%)	152$\pm$2

Table 12. Table 12: Measured reactor neutron induced fluence rate outside the shield compared to the neutron fluence rate at the surface of one CONUS HPGe diode inside the shield from MC for maximum thermal power of the reactor. The measured neutron spectrum inside A408 has been used as input for the simulation. The definition of the E n subscript 𝐸 n E_{\text{n}} regions is identical to Table  5.2.1 .

$E_{\text{n}}$ region	n outside shield [cm-2d-1]	n arriving at diode [cm-2d-1]	first n [cm-2d-1]
thermal	597$\pm$39	(0.39$\pm$0.04)$\cdot$10-3	(0.36$\pm$0.04)$\cdot$10-3
intermediate	142$\pm$19	(1.67$\pm$0.01)$\cdot$10-3	(1.38$\pm$0.01)$\cdot$10-3
fast	7$\pm$5	(0.17$\pm$0.03)$\cdot$10-3	(0.14$\pm$0.03)$\cdot$10-3
\hdashline total	745$\pm$30	(2.24$\pm$0.10)$\cdot$10-3	(1.89$\pm$0.10)$\cdot$10-3

Table 13. Table 13: Expected count rate by reactor neutrons inside the CONUS shield for the maximum reactor thermal power of 3.9 GW compared to the measured background during reactor OFF time.

energy	MC	measurement
keVee	[kg-1d-1]	[kg-1d-1]
$[0.3,0.6]$	0.006$\pm$0.002	12$\pm$1
$[0.6,11]$	0.025$\pm$0.005	148$\pm$2
$[11,400]$	0.15$\pm$0.03	716$\pm$16

Equations

$$\text{n}+{}^3\text{He}\to {}^3\mathrm{H}+\mathrm{p}+\mathrm{Q}\text{, with Q=764keV.}$$

$${}^{10}\mathrm{B}+\mathrm{n}\to {}^7\mathrm{Li}+\alpha \text{.}$$

$${}^{59}\mathrm{Co}+\mathrm{n}\to {}^{60}\mathrm{Co}+\gamma \text{,}$$

$$N_{p,i}^{(1)}=\frac{C_i^{(1)}}{E_{\text{KBR,}i}},E_{\text{KBR,}i}=\sum _j{P}_{\text{KBR,}j}\cdot t_j,$$

$$N_i^{(2)}=\frac{C_i^{(2)}}{t_i},$$

$$P_{\text{KBR}}^{\text{DS-3 mean}}=(0.89\pm 0.02)\cdot P_{\text{KBR}}^{\text{max}}=(3.47\pm 0.08)\text{GW}.$$

$$E_{\text{KBR}}^{\text{DS-3 mean}}=3.47\text{GW}\cdot 24\text{h}=83.3\text{GWh},$$

$${\Phi }_{\text{mean}}^{\text{(res)}}(E_{\text{n}})={\Phi }_{\text{mean}}^{(1)}(E_{\text{n}})-{\Phi }^{(2)}(E_{\text{n}}),$$

Full text

††journal: Eur. Phys. J. C

1 Introduction

Coherent elastic neutrino nucleus scattering (CE$\nu$NS) is a purely neutral weak interaction with a large variety of physics applications. These span from supernovae dynamics and nuclear form factors to the search for phenomena beyond the Standard Model: deviations from the Weinberg angle at MeV scale, electromagnetic properties of neutrinos as well as non-standard interactions in the neutrino-quark sector. Even though predicted in 1973 Freedman:1973yd , CE$\nu$NS has eluded detection for more than four decades mainly due to technological difficulties in observing tiny nuclear recoils below few keVee of ionization energy. It was observed for the first time in 2017 by the COHERENT experiment Coherent:2017 . Furthermore, the demand for very intense neutrino fluxes e.g. pion-decay-at-rest sources or commercial nuclear reactors, requires that the experiments are built close to these neutrino sources. At such shallow depth locations, several background components can aggravate the attempt of detecting CE$\nu$NS.

CONUS is a novel experiment which aims at detecting CE$\nu$NS signals using reactor antineutrinos. Since April 1, 2018, it is operational at the nuclear power plant in Brokdorf (Kernkraftwerk Brokdorf; KBR) PreussenElektra , Germany, where it is located at an average depth of 24 m of water equivalent (m w.e.) and 17.1 m distance to the reactor core center. Four ultra-low threshold, high-purity germanium (HPGe) detectors are embedded in a multi-layer shield, profiting from decades-long developments for low-background Ge $\gamma$-ray spectroscopy Heusser:1995wd ; Heusser:2015 at the Max-Planck-Institut für Kernphysik (MPIK) in Heidelberg, Germany. While for most applications (such as the selection of intrinsic radiopure materials) neutron-induced backgrounds were not critical so far, these become relevant for CONUS-like experiments. Thus, all potential neutron sources at the KBR reactor site had to be inquired first: cosmogenic neutrons induced by muons in the reactor building and in the CONUS shield; neutrons from the spent fuel storage pond above the experiment; ($\alpha$,n) reactions from natural radioactivity in the surrounding concrete walls and basements; neutrons from the reactor core; and $\gamma$-radiation from neutron-induced isotopes decaying along the primary coolant of the pressurized water reactor. Whereas the first three classes are steady-state sources, the latter two are potentially troublesome. Both can mimic CE$\nu$NS signals, since they are correlated with the thermal power and can contribute counts to the region of interest. Quantifying these backgrounds via independent measurements and determining their impact on the CONUS HPGe detector energy spectra are of fundamental importance. In order to achieve a high accuracy, the CONUS collaboration and the Neutron Radiation Department of the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig, Germany, developed an extensive measurement program and validation procedures. The multi-variate approach included neutron and $\gamma$-ray detection techniques, multiple measurement campaigns during reactor ON/OFF times at the experimental site, scans of different room positions, measurements inside and outside the CONUS shield, measurements at the reactor site and at the MPIK underground laboratory under similar overburden conditions, and the deployment of high and low activity 252Cf neutron sources. In addition, Geant4-based Monte Carlo (MC) simulations were performed for all these configurations. In a first step, the measurements helped to validate the MC code in terms of neutron generation and propagation. In a second step, the MC simulations were used to support and interpret the neutron measurement results in detail. Finally, they were used to predict the impact of the measured thermal power correlated neutrons and $\gamma$-ray flux on the CONUS HPGe detectors.

This article focuses on the neutron (direct) and neutron-induced $\gamma$-ray (indirect) measurements and related MC simulations for the CONUS experimental site. The article is structured as follows: Section 2 describes the direct and indirect neutron detection techniques and the thermal power determination. Section 3 presents the reactor environment and Section 4 the implementation of the reactor simulation. In Section 5, the Bonner sphere neutron measurements and the results including the comparison to MC expectations are discussed in detail. In the same way, the measurements with the HPGe spectrometer CONRAD including the comparison to MC are summarized in Section 6. Finally, Section 7 describes the MC simulation of the measured neutron field and $\gamma$-ray background passing through the CONUS shield to investigate the impact of the neutron-induced signals on the energy spectra of the CONUS detectors.

2 Description of neutron sensitive devices used in this work

2.1 Direct neutron detection

A Bonner sphere Spectrometer (BSS) Thomas2002 ; Alevra2003 consists of a set of moderating spheres with different diameters and a thermal neutron sensor that is placed at the centre of each sphere. Each sphere plus thermal sensor combination has a different energy-dependent response to neutrons. The peak of the neutron response function shifts to higher neutron energies as the size of the moderator increases (the responses of the Bonner spheres used for the measurements at KBR are shown in Figure 1). It is usual practice to measure also with the thermal neutron sensor without a moderating sphere (i.e. the bare detector).

The measurements of the neutron background at KBR were carried out with the BSS NEMUS Wiegel2002 of PTB. It consists of ten polyethylene (PE) spheres with diameters111In this paper we use the convention of labeling each Bonner sphere by its diameter in inches, $1\,\text{in}=2.54\,\text{cm}$. 3, 3.5, 4, 4.5, 5, 6, 7, 8, 10 and 12 ”. The set also contains a bare detector (diameter 3.2 cm), a Cd-covered detector, and four modified spheres with lead (Pb) and copper (Cu) shells. Thanks to the metal, embedded in the PE spheres, the response functions dramatically increase for neutron energies above $E_{\text{n}}\sim 50$ MeV. The central thermal neutron sensors are spherical 3He-filled proportional counters (type SP9, company Centronic Ltd. he3counter ), detecting the thermalized neutrons via the reaction:

[TABLE]

For the measurements carried out at KBR, we used SP9 counters with 3He pressure of $\sim 200$ kPa. In order to cover the complete energy range of the expected neutron field and yet minimize the required measurement time, we chose a minimal subset of spheres, namely a bare counter, 3, 4.5, 6, 8, 10 and 12 ”, plus the modified sphere of 8 ” diameter containing a Pb shell of 1 ” thickness. The inclusion of the modified sphere improves the spectrometric properties of the system at higher energies and allows to check for the presence of high-energy cosmic-ray induced neutrons ($E_{\text{n}}\sim 100$ MeV Wiegel2002b ), even though due to the massive concrete shield above the CONUS site their contribution is expected to be very small.

In general, the neutron count rates measured at KBR were very low, of the order of $\sim 10$ counts per hour and detector, or less. To determine the number of neutron-induced events in the pulse height spectra (PHS) recorded with the SP9 counter, the procedure, previously developed for measurements in underground laboratories Zimbal2013 ; Reginatto2013 ; Reginatto2018 , was applied. Figure 2 shows a typical PHS, together with the fit function to describe the PHS shape and to extract the neutron signal from background.

2.2 Indirect neutron detection

HPGe spectrometers with and without shield can be used to indirectly gain information on neutron fluences. This is possible by the detection of the $\gamma$-rays emitted after neutron capture either in the vicinity of the Ge detector or in the detector material itself. Mostly thermal neutrons are captured, but there is also a contribution from higher energetic neutrons (see Figure 3).

Without any shield, $\gamma$-rays from neutron capture in the building structure (e.g. reinforced concrete with steel) can be seen by the HPGe detector. The spectrum below 2700 keVee is dominated by natural radioactivity, but for neutron captures, higher energetic lines at up to $\sim$10 MeV are emitted, where nearly no other background is expected. From the resulting spectrum, the isotopes found in the environment can be identified and from the $\gamma$-line count rate the neutron fluence rate can be estimated. In order to do this, MC simulations including the geometry of the detector and the location with the correct material compositions are required. In the MC simulation, the neutron captures are reproduced including the capture probability over the whole neutron energy range. The method is less precise than a direct measurement with Bonner spheres as described in Section 2.1, but it allows to estimate independently a fluence, to support results from direct measurements or to validate a MC simulation. For the CONUS experiment, this is done in a measurement with the CONRAD (CONus RADiation) HPGe spectrometer at the location of the nuclear power plant. The results can be found in Section 6.

Gaining information from neutron capture is mandatory, if a direct measurement is not possible e.g. to study the neutron fluence at a HPGe diode within a shield that cannot be opened anymore. While the $\gamma$-radiation from outside is highly suppressed, lines from neutron capture within the shield material as well as in the Ge of the detector become visible. At shallow depth, many of these lines are induced by the neutrons created via muon capture inside the shield. There can also be contributions from neutrons fluences from outside propagated through the shield. To be able to detect these $\gamma$-lines, a low background level within the shield is required. This is usually achieved by applying a muon anti-coincidence system (so-called "muon veto"). In this way, especially $\gamma$-lines from metastable Ge states with half-lives longer than a veto window in the range of a few hundred ${\mu}$s become clearly visible Heusser:2015 . Once again, the neutron fluence can be estimated from the $\gamma$-line count rate or measurements of the line count rates can be used to validate the neutron production inside the shield in the MC simulation. This has been done for a detector at the MPIK laboratory in detail hakenmueller:masterthesis . For the CONUS experiment, this will be featured in an upcoming publication.

In addition to neutron capture, neutrons in Ge can also undergo inelastic and elastic scattering depending on their energy. In these interactions, there will be Ge recoils with an identical signature as the one for CE$\nu$NS. Thus, this highly relevant background for the CONUS experiment will be discussed in detail in Section 7.

2.2.1 Specifications of the HPGe spectrometer CONRAD

For background studies without shield at the reactor site the ultra-low background p-type coaxial HPGe detector CONRAD ($m=$2.2 kg), with the diode refurbished by Mirion Technologies, Canberra Olen canberraolen , is employed within the CONUS experiment. It has been used furthermore for background studies inside the CONUS shield during the commissioning phase of the experiment at the MPIK underground laboratory. The large detector mass is beneficial to especially detect high energetic $\gamma$-lines up to $\sim$11 MeVee as the detector also has a high geometric detection efficiency at these energies. To be allowed to set it up at KBR, the detector was upgraded with an electrical cryocooling system.

The detector has an active mass of (1.90$\pm$0.15) kg, which was determined as described in Heusser:2015 , budjas2009 , TobiasMasterarbeit . The thickness of the inactive layer at the diode surface has been evaluated from the ratio of the absorption of 241Am $\gamma$-lines at different energies compared to a MC simulation and amounts to (2.5$\pm$0.1) mm. Moreover, to adjust to the measured line count rates from 60Co measurements in different positions, the bore hole dimensions were adapted. All in all, 85% of the Ge crystal are active.

With the help of pulser scans over the whole energy range up to 11 MeVee it could be confirmed that the detection efficiency due to electronics is constant over the whole spectral range. Furthermore, the peak position has been found stable within 1 keVee over a period of 2 months. A small non-linearity within the energy scale has been discovered making it necessary to calibrate separately the two energy regions, where $\gamma$-lines have been observed (below 2700 keVee and above 4500 keVee), with two linear functions.

2.2.2 Specifications of the CONUS HPGe spectrometers

The CONUS experiment employs four 1 kg ultra-low-background p-type point contact HPGe spectrometers equipped with an electrical cryocooling system (manufactured by MPIK and Mirion Technologies, Canberra Lingolsheimcanberralingolsheim ). This is beneficial for a low noise threshold required to detect CE$\nu$NS as well as for the reactor environment, as no cryogenic liquids for cooling the diodes are allowed there. With various source and background measurements, the characteristics of the detectors have been determined and will be described in an upcoming publication. In the course of this publication, the specifications of detector 1, referred to as C1, are used exemplary to determine the expected measured spectrum of reactor neutrons at the diode. As for the CONRAD detector, the active volume has been determined from the 214Am source measurements at different positions compared to MC simulations. An inactive layer on the side and on top of the diode at the opposite of the point contact is assumed. While the detector is completely inactive at the diode surface, i. e. inside the so-called "dead layer", this is not true for the transition layer, i. e. the volume in between the dead layer and the active volume of the diode. In this transition layer, the charge collection efficiency decreases continuously towards the diode’s surface. Thus, energy depositions outside of the active volume can induce counts in the spectrum, but these so-called "slow pulses" will be reconstructed at energy values below the original energy. The effect can be observed clearly in the energy range below the 59.54 keV peak of the 214Am source measurements. Assuming a sigmondial shape for the decreasing charge collection efficiency in the MC of the source measurements as suggested in Queching:Bscholz , the thickness of the transition layer can be evaluated by varying it and comparing the resulting shape to the source measurements. For C1, this amounts to about 30% of the total layer thickness. The information is employed to correctly describe the spectral shape of a background contribution. Subtracting transition and dead layer, an active mass of (0.94$\pm$0.03) kg is determined.

Moreover, with the help of pulser measurements the detector response towards the noise threshold was studied. The detection efficiency decreases towards the noise edge at around 300 eVee.

2.3 Neutron flux-correlated reactor instrumentation

2.3.1 Absolute thermal power

For a good estimation of the neutrons emitted in the reactor core as well as a precise prediction of the neutrino flux, one of the crucial reactor quantities is the thermal power. The thermal power in a nuclear reactor is given by the number of fissions times the energy released per fission summed over all fission isotopes. The relevant contributions are coming from the two uranium (U) isotopes, 235U and 238U, as well as the two plutonium (Pu) isotopes, 239Pu and 241Pu.

The absolute thermal power of a commercial pressurized water reactor (PWR) as in Brokdorf is determined by monitoring the heat flow in the secondary circuit. The most relevant parameters in this calculations are the mass flow of the feed-water in the secondary circuit of the reactor and the specific enthalpy rise in the steam generator. Corrections have to be made for losses in the primary and secondary circuits e.g. due to radiation and convection or for contributions of the circulation pumps. Those have only minor impact on the final uncertainty of the thermal power estimation, since they account for less than 1% of the total power. The maximal thermal power of KBR at full operation is 3.9 GW corresponding to a gross electrical power output of 1.47 GW.

The systematic uncertainties on the thermal power estimation are summarized in Table 1. The enthalpy rise can be calculated from steam tables using measured values of pressure, temperature and moisture content around the steam generator. The feed-water is circulated at a rate of about 2000 kg s*-1*. The temperatures of the water and steam are determined before and after the steam generator. The systematic uncertainty on the thermal power associated to those measurements is 0.54%. The moisture content of the steam contributes with 1.56% to the total uncertainty.

The dominant contribution on the uncertainty of the thermal power is given by the mass flow measurement. The flow meter used at KBR is operated on the principle of the Venturi effect and has an uncertainty of 1.64%. From the combination of those uncorrelated contributions by quadratic summation, a total uncertainty on the absolute thermal power of 2.3% ($1\sigma$) is obtained. The statistical variations of the thermal power measurements during a cycle are on a negligible level of about 0.1%.

The thermal power determination in the secondary circuit is rather insensitive to fast changes and provides no spatial information about the situation inside the reactor core. The spacial distribution and power variations are therefore determined using ex-core and in-core neutron flux instrumentation (see Section 2.3.3 and Section 2.3.2). Especially the fast neutron flux in the ex-core instrumentation is an indicator for the local thermal power generation.

2.3.2 Ex-core instrumentation

The ex-core instrumentation is situated in the concrete shield (so-called "biological shield") around the reactor core as shown in Figure 4. To be able to cover more than 14 orders of magnitude of neutron flux the instrumentation consists of three different systems. Two of them use ionization chambers and one uses proportional counters. The counting gas in all systems is BF3. The neutrons are detected via the reaction

[TABLE]

One of the systems based on ionization chambers is able to cover the full range of the thermal power from 0 to 100% and provides a linear relation between the thermal power and the neutron flux. The chambers are placed in 4 radial positions around the core. The system consists of two chambers, connected in parallel, monitoring the upper half of the core and two chambers, connected in parallel, monitoring the lower half. There are basically three parameters having an impact on the detected signal: the relative power of neighboring fuel assemblies, the temperature of the coolant and the boron (B) concentration of the coolant. Therefore regular calibration of the system is needed, since the B concentration is decreasing over a cycle and the coolant temperature can vary e.g. in stretch-out operation of the reactor. In-between calibrations, these dependencies introduce a systematic uncertainty of up to 1.5%. In combination with a 2.5% statistical uncertainty, an overall uncertainty of the ex-core instrumentation of 3% is estimated. The proportional counters and the logarithmic range are only used while inducing criticality at the beginning and end of each reactor cycle, when the reactor is turned on and off respectively.

2.3.3 In-core instrumentation

The in-core instrumentation is positioned inside the guide tubes of certain fuel assemblies not occupied by control rods. Two systems exist. Eight fuel assemblies are each equipped with six so-called "self-powered neutron (SPN)" detectors, distributed axially over the length of the core. They rely on the reaction

[TABLE]

where the $\gamma$-radiation generates an electrical potential due to the photoelectric effect. The subsequent current in the measuring chain is proportional to the neutron flux. The 48 SPN detectors continuously monitor the radial and axial power distribution in the core. After appropriate calibration they show the maximum power per rod length unit (W/cm) in their respective surveillance region. Furthermore, in the so-called "aeroball measuring system" (AMS) guide tubes of 28 fuel assemblies (one tube in each assembly) are equipped with double pipes entering through the reactor vessel lid down to the lower end of the fuel assembly. During measurement a column of about 3000 steel balls (diameter 1.7 mm) containing 1.5% of Vanadium (V) is inserted into the core, where the 51V is partially activated to 52V (T1/2=3.75 min) for about three minutes. The amount of activation is proportional to the thermal neutron flux at the point of activation and hence to the local reactor power. At 32 axial measuring points (so-called "parcels") the 1.4 MeV $\gamma$-ray emitted by 52Cr as $\beta$ decay product of 52V is measured. Semiconductor detectors are used to discriminate the signal delivered by interfering nuclides such as 56Mn and 51Cr. Thus, a 3D map of relative power distribution in the core can be created. The values for fuel assemblies not instrumented are extrapolated from the 28 instrumented ones. An example for such a (radial/polar) distribution is shown in Figure 5. The relative contribution of each fuel assembly to the total power is given. Summing up all contributions amounts to 193, the total number of fuel elements. The AMS is used on demand, typically twice per week, to calibrate the SPN detectors and to calculate the position dependent reactor burn-up. KBR operates a core simulator (POWERTRAX/S powertrax , designed by FRAMATOME GmbH), relying on the same technology that is used for core design. Based on various plant data like temperatures, thermal reactor power and control rod insertion depth, the simulator is capable of providing an online 3D image of the power distribution in the core. Calculations are done automatically, usually every two hours and more frequently in case of transients. The results are stored and can be displayed down to the level of a single fuel rod (236 being contained in each fuel assembly) and the 32 axial parcels. Thus, the local origin of neutrons and neutrinos escaping the reactor core and arriving at the CONUS experimental site can be calculated in detail.

3 Description of the environment

3.1 Experimental site at KBR

3.1.1 Overburden

During the commissioning phase of the CONUS experiment, the shield with a varying combination of detectors has been set up at the underground laboratory at MPIK. In this way, it was possible to characterize the experimental site in Brokdorf relative to the well-known conditions at the MPIK laboratory. At KBR, an overburden to shield against cosmic rays is provided by the concrete and steel structures of the reactor building. The whole building is enclosed in a concrete dome of 1.8 m thickness and the safety containment consists of a steel sphere of 3 cm wall thickness. The room A408, where the CONUS experiment is set up, is located in the lower hemisphere of the dome with more concrete around from the walls of the surrounding rooms and above. The concrete density is 2.55 g cm*-3*, with different steel contents ranging between 0.8% for room divider walls and 3.2% for the biological shield surrounding the reactor core. The hydrogen content, highly relevant for the moderation of neutrons, was determined via element analysis. The sample was taken from small concrete pieces, which were removed from the floor of room A408 during the installation of the CONUS experiment. The analysis reveals a hydrogen content of (0.8$\pm$0.1)% concrete_analysis . Moreover, as it can be seen in the blue contours in Figure 6, the room A408 is located partially below the water pond of spent fuel assemblies and fully below the smaller pond used for loading the spent fuel storing casks prior to shipment, with contributions to the overburden. They are permanently filled with borated water to a level of 13.4$\pm$0.1 m (mean value over 7.5 months), even if the filling with spent fuel assemblies is varying. This leads to a variability in the mean density between 1.0 and 1.55 g cm*-3* (maximal allowed filling of the pond). These changes in overburden are considered negligible for the CONUS experiment. All contributions add up to an overburden of 10-45 m w.e. depending on the solid angle, meaning that the rather variable hadronic component of the cosmic rays at Earth‘s surface is fully suppressed. The effective overburden for the suppression of the cosmic-ray muon component can be determined by comparing the measured spectra inside the passive shield of the CONUS experiment without the muon veto system measured at the MPIK laboratory and at the nuclear power plant as displayed in Figure 7. The scaling factor over the whole energy range between both locations amounts to 1.62$\pm$0.02. The MPIK laboratory has a well-known overburden of 15 m w.e hakenmueller:masterthesis leading to an effective overburden of 24 m w.e. at KBR. The spectral shape agrees over the whole energy range, meaning that the same physics processes for the muon and muon-induced neutron interactions are relevant at both places.

3.1.2 Natural radioactivity

Measurements with HPGe spectrometers without any shield are dominated by the environmental radioactivity and anthropogenic isotopes from the surroundings. Two comparable measurements at the MPIK underground laboratory as well as in room A408 at the nuclear power plant were carried out with a CONUS detector. Comparing the integral count rate in the range of [20,440] keV, it was found that the background level at KBR is higher by a factor of 4.2$\pm$0.1 with respect to the MPIK laboratory. The difference between the locations is partially explained by the special attention that had been paid on employing concrete especially low in radioactivity at the MPIK laboratory location:Heusser1992 . To test the concrete at reactor site, the activity of the small pieces of concrete was measured at the screening station in MPIK laboratory Heusser:1995wd . In Table 2, the results are compared to the measured activities from the concrete of the MPIK laboratory. For U and thorium (Th), comparable results were found, while the kalium (K) content is lower in the MPIK sample. There is also a finite contamination of man-made 137Cs inside the concrete from Brokdorf. Moreover, contrary to the MPIK laboratory, highly varying 60Co concentrations were observed in the samples and thus a range is given in Table 2. This could be a surface contamination, as 60Co has also been observed in the dust in radio protection-related measurements similar to other nuclear reactors elsewhere texono2017 .

Furthermore, there is an additional background contribution at reactor site originating from reactor neutron interactions inside the water of the cooling cycle and neutron capture in concrete. These $\gamma$-rays have been measured with the CONRAD detector and will be discussed in detail in Section 6.

3.1.3 Distance to reactor core

The distance of the CONUS experiment’s shield center in room A408 of KBR to the middle of the reactor core amounts to (17.1$\pm$0.1) m, ensuring a high reactor antineutrino ($\overline{\nu}_{e}$) flux at the experimental site. The experiment is nearly at the same height as the reactor core with an offset along the z-axis of 0.25 m. The HPGe diodes have a distance of $\sim$50 cm from the floor of A408. The reactor core consists of 193  fuel assemblies contained in a cylinder of 3.45 m diameter (see Figure 5) with an active length along the z-axis of 3.9 m. Details about the materials and geometry between the reactor core and room A408 are given in Section 4.

4 Description of the MC simulation framework

The MC simulation framework MaGe MC:mage , based on Geant4 (version Geant4.9.6p04) MC:geant4_1 ; MC:geant4_2 is applied to support the understanding and to complement the neutron measurements via an ab initio calculation. In a first step, the neutron propagation from the reactor core to room A408 is simulated as well as the propagation of neutrons from the spent fuel assemblies inside the storage pool above room A408. In the second step, the neutrons arriving in A408 are propagated through the CONUS shield towards the HPGe diodes employing the measured neutron spectrum inside A408 as input. The relevant neutron interactions, models in Geant4 and the applied cross section data sets are listed in Table 3.

4.1 Implementation of geometry

4.1.1 Nuclear power plant and room A408

From construction plans, the overall structure and main concrete parts of the reactor building were implemented using the information on the concrete from Section 3.1.1. The reactor as starting point of the neutrons was modeled in detail, including all the 193 fuel assemblies. In the MC, these are approximated by four fuel rods instead of the 236 as in reality, each made up of Zirconium alloy cladding tubes filled with UO2 pellets. The size of these fictive fuel rods was chosen so that the overall mass of a fuel assembly is reproduced correctly. The reactor core is filled with borated water with a B concentration of 500 ppm of enriched 10B (1% boric acid, 99% water) as expected in the middle of a reactor cycle. A mean water temperature of 320*∘C and a pressure of 15.7 MPa have been assumed, leading to a water density of 0.687 g cm-3* waterdensitytable . The reactor core is contained inside the reactor pressure vessel (RPV) made from ferritic steel with a thickness of at least 25 cm. Eight openings can be found at the top of the reactor core for the loop pipes leading the water from the core to the steam generators, where they heat up the water in the secondary cycle, and afterwards return it to the core. For simplicity, only the two loop pipes on the side of room A408 have been implemented into the MC geometry. The reactor core is enclosed by the biological shield and heat insulation amounting to more than 2 m of concrete thickness in total. This is followed by an empty room around the biological shield. In the geometry, not all details of this space were implemented, but special attention was paid to ensure this area to be closed to all sides to allow for backscattering of neutrons. Adjacent to this space behind a concrete wall of 1.3-1.45 m thickness, the room A408 can be found. The interior was modeled as in Figure 6. Also steel doors are included as well as the concrete walls of the neighboring room. Room A408 has a height of 2.8 m and the concrete ceiling, which is also the floor of the spent fuel storage pool, has a thickness of 1.85 m. The spent fuel storage pool and the cask loading pond are lined with several centimeters of steel and filled with 13.3 m of borated water. Between the active part of the spent fuel assemblies and the floor of the pool, there is a distance of about 80 cm. The amount of spent fuel assemblies within the storage pool is variable in the MC. The 10B content is constantly 2300 ppm (5% boric acid, 95% water). The most important features of the implemented geometry including the location of the middle of the CONUS shield can be found in Figure 8.

4.1.2 Geometry of CONUS shield and HPGe detectors

The CONUS shield was implemented in detail in the MC (see Figure 9) inside the geometry of room A408 (see Figure 8). To suppress exterior $\gamma$-radiation, 25 cm of Pb in all directions are employed. Moreover, there are two layers of in total 10 cm of borated PE (3% equivalent of natural B) to moderate and capture neutrons from outside as well as neutrons created by muons in the Pb layers of the shield. The plates were produced from PE and boric acid H3BO2, enriched in 10B, which has an especially high neutron capture cross section compared to other isotopes. Neutrons are also moderated by two polyethylene plates (5 cm each), one on top of the shield and one in the layers below the detector chamber. For the active muon veto system, organic plastic scintillator plates (thickness: 5.2 cm) equipped with photo-multiplier tubes (PMTs) are included in the shield. These plates also contributes to the moderation of neutrons. Inside this shield, the four CONUS detectors are placed within the detector chamber with a volume of 25 l. The Cu cryostats and their interior, including the point-contact HPGe diodes and supporting structures are modeled in the MC geometry as in the technical drawings.

Similarly, the coaxial HPGe CONRAD detector without any shielding is modelled by setting up the detector’s Cu cryostat with cooling finger and its full interior inside the MC geometry in front of the wall adjoined to the space around the reactor core as it was positioned for the measurement (see Figure 6).

4.1.3 Input spectra and output for reactor neutron MC

At a nuclear power plant, neutrons are created predominately inside the reactor core via fission and immediate evaporation from fission products. Over the whole cycle, more than 50% of the fissile material is made up of 235U, while 238U, 239Pu and 241Pu contribute as well MCnorm:Kopeikin2004 . The 235U neutron fission spectrum according to a Watt distribution function is displayed as black line in Figure 19, with a mean neutron energy of 1.95 MeV book:reaktortechnik . As the neutron spectra of the main other isotopes undergoing fission such as 239Pu are very similar, in MC simulation the 235U fission spectrum is employed as initial spectrum for the neutrons. Most of these neutrons are moderated within the reactor core and induce fission again, fueling the chain reaction employed to create the power output of the reactor. However, about 10*-4* of the neutrons will leave the reactor core before they either hit fissile material, are absorbed in the fuel assemblies’ structures or are moderated enough to induce another fission (see Table 9). This is most likely to happen at the border of the reactor core, thus justifying to start neutrons only within the volumes of the UO2 pellets of the first and second outer-most ring of fuel assemblies in the MC simulation (in total 104 of 193 fuel assemblies). For the purpose of the propagation outwards from the reactor core, the ongoing fission reactions are not required and consume computation time, thus all fission products are killed immediately by the MC. Due to the huge decrease of the neutron flux along the way towards room A408, the MC simulation has been split into four steps where the spectrum of neutrons passing a certain geometric boundary was registered and used as a new input spectrum for the next part of the MC simulation (see Figure 8 for the single steps denoted with I-IV). In the end, the spectrum of the neutrons leaving the walls adjoined to the space around the reactor core is recorded. Moreover, the neutrons hitting a 6” diameter air sphere at about the location of the middle of the shield of the CONUS experiment are tracked to be compared to and to be used in the analysis of the BSS data. The device itself is not simulated, since the conversion to the measured PHS is carried out by the response functions as described in Section 2.1. Alternatively, to represent several spheres set up at the same time, the neutrons passing through a fictional horizontal air plate (size: 2 m$\times$3.5 m) are accounted for. Furthermore, for the CONRAD detector measurements, the last step is repeated with this detector present inside room A408. All hits inside the HPGe detector are registered. The decreased charge collection efficiency outside the active volume is added in the post-processing.

Besides the reactor core, neutrons are also emitted by the spent fuel assemblies in the storage pool above the CONUS experiment. The majority of the neutrons are emitted by actinides, especially by 244Cm, while other isotopes only contribute to a few percent reviewspentfuel1986 . Thus the Watt distribution function for 244Cm is used as initial spectrum. Assuming the storage pool is filled with the maximum number of fuel assemblies, neutrons were started from the volume of those 192 fuel assemblies located above room A408 and registered in the horizontal air plate described above.

4.2 Initial spectrum and output for the particle propagation through the CONUS shield

Assuming a homogeneous neutron flux inside A408, neutrons are started isotropically from a hemisphere (diameter=1.4 m) spanning around the CONUS shield towards the floor. To take into account backscattering effects, the walls, ceiling and floor of room A408 are included in the simulated geometry (see Figure 8). The measured neutron spectrum in the exact location of the CONUS experiment is used as input for the neutron energy (see Figure 18). The neutrons are propagated through the CONUS shield. All neutrons arriving at the HPGe diodes are registered. Moreover, all energy depositions inside the HPGe volume are saved as well as the identity of the particles responsible for the energy deposition. No dead layer is assumed and the charge collection efficiency in the different sub-volumes of the HPGe diode is added in the post-processing. For the CONUS experiment the region of interest lies in the very low energy range of the spectrum (below 1 keVee) and thus in this simulation the secondary production cuts are lowered to 1.2 keVee for $\gamma$-rays and 850 eVee for electrons and positrons, increasing the computation time. This means that below these thresholds, the particles will not produce further secondary particles, but the whole remaining energy will be deposited directly in one location. For hadronic processes there is no such threshold.

Additionally to the neutron propagation simulation, also the measured $\gamma$-ray background inside A408 (see section 6) has been used as MC input. Mono-energetic $\gamma$-rays were started from the wall closest to the reactor core and the resulting spectrum inside the CONUS diodes was evaluated. All in all, more than 104 d in CPU time have been spent on the propagation of the neutrons through the reactor building geometry and the CONUS shield.

4.2.1 Validation of MC

For a reliable MC result, it is important to validate the physics processes involved. In MaGe, for electromagnetic interactions this has been done among others for source measurements in Heusser:2015 and budjas2009 as well as Poon2005 , Hurtado2004 and Amako2015 , for muon-induced interactions in hakenmueller:masterthesis .

For neutrons, however, there are in general much less validation campaigns available. The propagation of neutrons through shield materials have been examined at the MPIK by carrying out 252Cf source measurements within and in front of the CONUS shield and a similar shield of another HPGe spectrometer, GIOVE Heusser:2015 . The correct propagation of the neutrons through the shield was confirmed.

An overall good agreement for the isotopes relevant here for the probability of the number of emitted $\gamma$-rays in neutron capture has been found (see table 4.2.1). Especially the relative branching ratio between the different $\gamma$-lines is in excellent agreement with the literature values. However, additional $\gamma$-lines occur in the de-excitation spectrum in the MC, that are not supposed to be created. This has to be corrected for by removing all MC events containing such $\gamma$-lines.

Moreover, if the isotopes produced in neutron capture are metastable, they are not created in the MC using Geant4.9.6. It is especially of interest to be able to simulate these $\gamma$-lines for the metastable Ge states as described in Section 2.2. To do this, the cross section has to be implemented manually into the code. A separate simulation has to be run to study the $\gamma$-line count rate to avoid to add the energy depositions from this metastable decays to the prompt contribution.