<figure><img src="image_1.png" /></figure>

HAL
open science

# Neutrons et Photons Prompts de Fission de l'Uranium 238 et 235 Induite par Neutrons jusqu'à 200 MeV

Thierry Ethvignot

► To cite this version:

Thierry Ethvignot. Neutrons et Photons Prompts de Fission de l'Uranium 238 et 235 Induite par Neutrons jusqu'à 200 MeV. Physique [physics]. Université de Bordeaux 1, 2010. tel-03954705

HAL Id: tel-03954705

https://theses.hal.science/tel-03954705

Submitted on 16 Feb 2023

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

Public Domain
Habilitation à Diriger des Recherches en physique

Thierry Ethvignot

Neutrons et Photons Prompts de Fission de l'Uranium 238
et 235 Induite par Neutrons jusqu'à 200 MeV

Date de soutenance : 27 mai 2010

Etablissement de soutenance : Université de Bordeaux 1

Jury : 
M. Gérard BARREAU, Directeur de recherche, 
Président du jury

M. Thierry GRANIER, Ingénieur-chercheur

Mme Fazia HANNACHI, Directeur de Recherches

M. Eric LIATARD, Professeur d'Université

M. Jean-Luc SIDA, Ingénieur-Chercheur
"To those of you who've received honors, awards and distinctions,
I say well done,
and to the C students...
I say, you too can be President of the United States"

George W. Bush

Cérémonie de remise de diplômes
Yale, mai 2001
# Table des matières

## 1 Synthèse de l'activité scientifique

1.1 Introduction

1.2 L'installation WNR, source intense de neutrons de spallation

1.3 Les mesures et X prompts avec GEANIE

1.4 Les mesures de neutrons prompts avec FIGARO

1.5 Conclusion

## 2 Articles publiés

2.1 Nucl. Intrum. and Meth. A490: Mise au point du détecteur de fragments de fission transparent aux X pour GEANIE

2.2 Nucl. Intrum. and Meth. A554: Technique de la compensation appliquée aux cellules solaires en milieu hautement ionisant

2.3 Pont d'Oye V: Résultats des mesures des distributions en charge et en masse avec GEANIE

2.4 Nucl. Intrum. and Meth. A523: Mise au point du détecteur de neutrons de fission FIGARO

2.5 Phys. Lett. B575: Mesure de l'énergie moyenne des neutrons de fission avec FIGARO

2.6 Phys. Rev. Lett. 94: Mesure de la multiplicité moyenne des neutrons de fission avec FIGARO

2.7 Phys. Rev. Lett. 101: Réponse à un commentaire de Kornilov et Hambsch

## 3 Annexe

Détection de particules alpha et résolution spatiale avec les cellules solaires
# Chapitre 1

## Synthèse de l'activité scientifique

### 1.1 Introduction

Le phénomène de fission, qui est au centre des applications énergétiques de la physique nucléaire, est encore mal compris. Au niveau théorique, de grosses divergences subsistent dans la description des propriétés de la fission, suivant les modèles et les approches utilisés. Au niveau expérimental, la fission induite par neutron a été peu étudiée au-delà de 14 MeV d'énergie incidente, faute de source adéquate. Tout au plus avait-on mesuré les sections efficaces de fission des actinides de longue période et le nombre moyen de neutrons prompts émis dans la fission jusqu'à 30 MeV. Ces recherches sont reliées aux applications des données nucléaires. Par exemple, elles sont requises pour les applications industrielles futures de la fission: réacteurs hybrides pour la production d'électricité et pour l'incinération des déchets, production de faisceaux exotiques par fission...

Avec la source blanche de neutrons d'énergie de quelques centaines de keV à quelques centaines de MeV, le laboratoire LANSCE à Los Alamos dispose de moyens uniques pour l'étude expérimentale de la fission nucléaire. Cette source de spallation, construite auprès d'un accélérateur de protons de 800 MeV, est opérationnelle depuis une quinzaine d'années. Elle est la plus intense au monde dans la gamme d'énergie qui nous intéresse, plus performante que les sources aux laboratoires GNEIS (Gat-china, Saint-Pétersbourg) et n-TOF (CERN, Genève). On voit sur la figure ¹ (page suivante) les flux comparés des installations WNR, n-TOF et GELINA (Geel) dans la gamme de 0,1 à 100 MeV. On a porté des valeurs utiles typiques au point cible. Le flux sur WNR est d'un à deux ordres de grandeurs supérieur aux flux des autres sources en service actuellement. Il est intéressant de constater que le flux projeté sur l'installation SPIRAL2-NFS à GANIL serait compétitif pour des neutrons de 5 à 25 MeV.
<figure><img src="image_2.png" /></figure>

<footnote n="1">¹Comparaison du flux moyen de neutrons disponible sur différentes installations. Compilation réalisée par F. Gunsing d'après : Coceva et al. NIMA489 et Pancin et al. NIMA524 pour n-TOF; Flaska et al. NIMA531 pour GELINA; Ledoux et al. rapport CEA-DAPNIA 05-40 pour SPIRAL2-NFS; http://wnr.lanl.gov/data/fluxdat.htm pour WNR.</footnote>
Le groupe de physique nucléaire expérimentale LANSCE-NS, composé d'une vingtaine de physiciens et techniciens, est chargé de recherches autour des réactions nucléaires induites par neutrons. Ils disposent pour ce faire de moyens expérimentaux associés très performants pour la détection des $\gamma$, neutrons et particules chargées émis dans les réactions induites par neutrons, comme nous allons le montrer plus loin.

J'ai ainsi proposé un programme nouveau de mesures des propriétés de la fission induite par neutrons à Los Alamos en 1998. Les propriétés de la fission induite par neutrons intéressent beaucoup les Américains, qui ont surtout apprécié l'apport d'idées nouvelles et le renfort en effectifs de l'équipe. En effet, j'ai obtenu une bourse d'Etudes et Recherches à l'Etranger de la Délégation Générale pour l'Armement afin de financer un séjour de longue durée à Los Alamos. La mission, initialement prévue pour un an, a été prolongée d'un an pour réaliser des expériences nouvelles qui n'avaient pas été envisagées au début du projet. Mon séjour a été marqué par deux événements dramatiques qui n'ont pas trop perturbé le bon déroulement des expériences: l'incendie géant qui a ravagé les forêts aux alentours de Los Alamos et l'attaque terroriste du 11 septembre 2001. Dans ce document, je résume l'activité scientifique durant cette période sur ce sujet. Cela a donné lieu à la publication d'articles scientifiques et techniques. Ces articles, au nombre de six, sont reproduits au chapitre 2. Dans le chapitre 3, on présente en annexe des études en cours avec les cellules solaires non encore publiées. Enfin, dans le chapitre 4, on trouve les renseignements scientifiques demandés: CV, liste de contributions orales en congrès internationaux, liste de participation à jury de thèse, liste de publications.

## 1.2 L'installation WNR, source intense de neutrons de spallation

WNR est une source pulsée de neutrons de spallation obtenus par le bombarde-ment d'une cible de tungstène par le faisceau de protons de 800 MeV de l'accélérateur linéaire du LANSCE. Le spectre des neutrons est compris entre 0,5 et 800 MeV avec toutefois une forte prépondérance pour les énergies inférieures à 30 MeV. L'inten-sité typique obtenue sur les aires expérimentales à 30 MeV $\pm$ 1,5 MeV est de 6000 neutrons.s$^{-1}$.cm$^{-2}$. Ce faisceau est délivré selon un mode impulsionel : une bouffée de protons toutes les 1,8 micro-secondes pendant 650 micro-secondes, ce schéma étant répété à la cadence de 100 Hz. L'énergie des neutrons est déterminée par la mesure de leur temps de vol. Les expériences GEANIE et FIGARO sont situées à une vingtaine de mètre en aval de la source. Ainsi, la résolution sur l'énergie des neutrons incidents dépend de leur énergie : quelques % à 1 MeV et quelques dizaines de % à 200 MeV.

Le but de l'expérience GEANIE a été de déduire la distribution en charge des fragments dans la fission de l'uranium 238 et 235 par des neutrons de 0.5 à 800 MeV grâce à la mesure du rayonnement X prompt. Celui de l'expérience FIGARO a été de mesurer les distributions en énergie et en multiplicité des neutrons de fission pour les mêmes systèmes.
## 1.3 Les mesures $\gamma$ et X prompts avec GEANIE

### Le détecteur GEANIE

Le multi-détecteur GEANIE constitue un outil unique d'investigation du rayonnement $\gamma$ et X associé aux réactions induites par des neutrons de hautes énergies. GEANIE est un ensemble de 26 détecteurs germanium répartis dans une géométrie $4\pi$. Afin de prouver la faisabilité de notre proposition au comité d'expériences, nous avons réalisé des tests avec une source de fission spontanée et un détecteur germanium planaire. Ce test a fait l'objet du stage que j'ai proposé à Jean-Philippe Amaral, alors en Magistère de Physique à Orsay (1998). Jean-Philippe a très clairement établi les avantages et les inconvénients de cette technique pour la mesure du rayonnement X prompt des fragments de fission.

Pour les expériences en fission induite par neutron avec GEANIE, nous avons utilisé 15 détecteurs coaxiaux de gros volume et de haute efficacité pour la détection des $\gamma$ de haute énergie. 11 autres détecteurs planaires de haute résolution ont été utilisés pour la détection des $\gamma$ de basse énergie et des X. Les 11 détecteurs planaires et 9 détecteurs coaxiaux étaient équipés de dispositifs anti-Compton au BGO et NaI. Deux chambres à fission (235U et 238U) de grand diamètre étaient disposées en amont de l'expérience afin de déterminer, hors ligne, le flux de neutrons incidents durant l'irradiation.

GEANIE avait été principalement utilisé dans le but de mesurer la section efficace de la réaction (n,2n) induite sur le plutonium 239. Cette expérience était réalisée en cible épaisse par mesure du rayonnement $\gamma$ en single, c'est-à-dire sans analyser les coïncidences $\gamma-\gamma$. Le rayonnement X n'était pas mesuré. Des modifications ayant trait à l'électronique associée au détecteur GEANIE lui-même ont du être effectuées afin de pouvoir mesurer le rayonnement X. De surcroît, afin d'optimiser l'efficacité de détection, une nouvelle configuration du détecteur GEANIE ainsi que du faisceau de neutrons ont été utilisés.

### Le détecteur de fragments de fission associé

Les fragments de fissions sont détectés à l'aide de cellules solaires disposées dans le faisceau de neutrons. La mise au point de cette cible a fait l'objet de publications (chapitre 2.1 et 2.2).

On verra que l'on a exploité un certain nombre de propriétés des cellules solaires afin de réaliser des expériences difficiles: faible épaisseur et capacité de fonctionner sans vide pour une transmission optimisée du rayonnement X de la fission; montage en compensation et robustesse pour s'affranchir du flash $\gamma$ et de la détérioration due aux fortes doses; capacité de détection $\alpha$ pour la discrimination $\alpha$-fission et des mesures (n,$\alpha$) et (n,p) futures; capacité de résolution spatiale grâce à une bonne résolution temporelle pour des études futures de corrélation de l'axe de fission avec le rayonnement associé. Ces deux derniers points sont en cours d'étude. Des résultats préliminaires sont portés en annexe (chapitre 3).

Dans la première publication (NIMA490), on décrit le détecteur de fragments de fission conçu pour la spectroscopie de photons de basse énergie auprès de la source blanche de neutrons WNR à Los Alamos. Il est constitué de huit couches de cellules solaires minces couvertes chacune d'un dépôt d'uranium 238 d'1 mg/cm². Ces dépôts ont été réalisés au CSNSM d'Orsay avec le séparateur SIDONIE. La pureté isotopique, déterminée par spectroscopie $\alpha$, est très élevée: une limite supérieure de 1 ppm d'235U a été établie. Le détecteur sert de cible active pour différencier les
événements de fission du bruit de fond et des autres réactions nucléaires. La faible épaisseur du détecteur par rapport à la transmission de photons de 20 à 50 keV a permis la mesure du rayonnement X des fragments prompts de fission. Des résultats préliminaires avec le spectromètre de photons GEANIE sont présentés.

La détermination de l'efficacité de détection a fait l'objet du stage de Lydie Giot, en DEA à Strasbourg en 2000. Elle a dû notamment réaliser les mesures avec un faisceau de neutrons pulsés de 14 MeV et mettre au point le programme de simulation de la perte d'énergie des fragments dans les cellules solaires. La réalisation de l'expérience à Los Alamos a impliqué l'intégration du système de détection des fragments au système d'acquisition de GEANIE. Cette intégration a ainsi nécessité un gros travail du fait du peu de versatilité du système d'acquisition de GEANIE, développé dans le but principal de l'étude des réactions (n,2n) par mesure du rayonnement en single.

## Les résultats obtenus sur les rendements de fission

Les données ont été acquises à la cadence typique de 30 fissions par seconde. Au total, 10 millions d'événements, en coïncidence prompte fission-photon (330 ns), ont été enregistrés. Le spectre X correspondant comporte plusieurs milliers d'évènements par éléments. Une analyse en fonction de l'énergie du neutron incident est en cours.

D'autre part, des données ont été prises avec une cible épaisse d'238U afin d'ex-
traire la section efficace de production d'un grand nombre de fragments de fission
par spectroscopie prompt.

Des résultats ont été présentés à la conférence Seminar on Fission, Pont d'Oye V, World Scientific (2004), p. 65, C. Wagemans, J. Wagemans and P. D'Hondt, Editors (chapitre 2.3). Des données similaires sur l'uranium 235 sont en cours de dépouillement. Une fois l'analyse terminée, les résultats seront ajoutés, et l'article sera soumis à publication dans Nuclear Science and Engineering.

Les rendements de rayonnement $\gamma$ et X K, émis dans la fission de l'uranium 238 induite par neutrons de 1 à 200 MeV, ont été mesurés pour la premières fois au Los Alamos Neutron Science CEnter. Les résultats sont utilisés pour étudier les fonctions d'excitations de production de fragments et la distribution de charge nucléaire des fragments primaires en fonction de l'énergie incidente. Ces estimations confirment la tendance d'une augmentation progressive de la probabilité de fission symétrique avec l'énergie des neutrons déjà observée dans les mesures de rendement en masse. Un bon accord qualitatif avec les systématiques de Wahl est obtenu. Ces résultats sont inclus dans un TecDoc de l'AIEA, fruit d'un groupe de recherches coordonnées auquel j'ai participé (2000-2003)

A l'aide d'une analyse détaillée du spectre X, on remonte au rendement indivi-
duel par élément dans la fission. A haute énergie, la distribution se symétrise. On
interprète cela comme une augmentation des voies de fission symétriques dues à la
plus grande disponibilité d'énergie d'excitation, de spin et d'états nucléaires en voie
de sortie.

Un certain nombre d'étudiants ont été associés à ces expériences: Patrick Pin et Jean-Francois Madrière (École Polytechnique Féminine), Cecille Goyon (Ecole des Mines de Nantes). Enfin, l'analyse détaillée de ces données a fait l'objet de la thèse de P. Casoli, soutenue fin 2003 à l'Université de Bordeaux. L'interprétation des résultats a nécessité le développement d'une collaboration avec les théoriciens de Bruyères-le-Châtel et de Los Alamos. Les développements de détecteurs de fragments basés
sur les cellules solaires se sont poursuivit, grâce notamment au stage post-doctoral de Michael Petit (voir chapitre 2.2 et 3).

## 1.4 Les mesures de neutrons prompts avec FIGARO

### Le détecteur FIGARO

Ces mesures avec des cibles d'uranium (grosses chambres à fission contenant 400 mg/cm² d'uranium) ont été réalisées sur la ligne de faisceau FIGARO. Cette ligne, spécialement conçue pour des mesures neutrons et $\gamma$ avec un faible niveau de bruit, peut accueillir de nombreux détecteurs de neutrons à liquide scintillant; six ont été utilisés pour les expériences sur 238U et 235U. Le détecteur est présenté au chapitre 2.4 de ce document. On y décrit le nouvel instrument "observateur de rayons $\gamma$ induits par neutrons rapides" (FIGARO) situé au Los Alamos Neutron Science Center. Il est conçu pour étudier les réactions nucléaires qui produisent de l'émission $\gamma$ et des neutrons auprès de la source blanche de neutrons WNR. Les neutrons et les rayons $\gamma$ émis sont respectivement détectés par plusieurs scintillateurs liquides et un détecteur germanium haute résolution ou un détecteur au fluorure de barium. A titre d'exemple, on présente les mesures de la diffusion inélastique de neutrons sur le silicium de 4 à 20 MeV, que l'on compare avec les prédicitions théoriques obtenues avec les modèles GNASH et EMPIRE II.

### Les résultats obtenus sur les énergies moyennes de neutrons de fission

Les mesures de neutrons de fission avec FIGARO ont nécessité une statistique importante correspondant à trois semaines de prise de données accumulées pour chacune des cibles d'uranium 235 et 238. Une série de mesures a aussi été effectuée avec une source de fission spontanée (252Cf) pour étalonner la chaîne de détection. Les données sous faisceau ont été acquises à la cadence typique de 500 fissions par seconde. La discrimination neutron-$\gamma$ est réalisée hors-ligne grâce à l'analyse de la forme du signal. L'énergie des neutrons incidents, tout comme celle des neutrons de fission, est déterminée par leur temps de vol. Les distributions en énergie en ont été extraites pour 50 bins d'énergie de neutrons incidents. Les résultats sont discutés dans le chapitre 2.5.

A des degrés divers, une étudiante et deux post-docs ont participé à ces études. Les études se poursuivent avec d'autres cibles. L'analyse de l'expérience avec le neptunium 237 est en cours.

Les spectres en énergie des neutrons émis dans la fission sont plus étendus à haute énergie incidente. Pour s'en convaincre, on a étudié la valeur moyenne du spectre en fonction de l'énergie incidente. Le creux observé vers 5 MeV est attribué à l'ouverture de la fission de deuxième chance. Le noyau d'uranium 239 émet un neutron puis fissionne. L'énergie d'excitation supplémentaire évacuée par les neutrons émis par les fragments diminue brusquement. Au-delà, l'augmentation de la valeur moyenne de l'énergie des neutrons émis est plus monotone, même si l'on devine un plateau pour la fission de troisième chance et quatrième chance vers 12 et 19 MeV. Les données sont comparées à un calcul effectué à Bruyères-le-Châtel. L'accord est très bon jusqu'à 20 MeV. Au-delà, une divergence apparaît. Le modèle et l'analyse sont en cours d'amélioration pour comprendre cet écart.
A 50 MeV et au-delà, les données suggèrent une augmentation légère de la température et de l'énergie cinétique des fragments.

## Les résultats obtenus sur les multiplicités moyennes de neutrons de fission

Les multiplicités de neutrons prompts de fission ont été mesurées pour la fission des uranium 238 et 235 induite par neutrons de 0.4 à 200 MeV. Les résultats sont présentés au chapitre 2.6. Les données sont très importantes pour l'incinération des actinides par réacteur hybride. Nous avons établi que la fission produit 10 neutrons de plus si elle est induite par des neutrons de 200 MeV par rapport à des neutrons de réacteur. La plupart des neutrons sont évaporés par les fragments de fission et le noyau composé de pré-fission. L'émission de pré-équilibre n'est responsable quant à elle qu'au maximum de 15% des neutrons prompts de fission à 200 MeV.

Les multiplicités mesurées ont aussi été interprétées avec un modèle “haute énergie”, générant des discussions approfondies avec les spécialistes du sujet, notamment V. Maslov (Minsk), D. Madland (Los Alamos) et A. Tudora (Bucarest). Il y a 10 neutrons de plus émis dans la fission à 200 MeV qu'à basse énergie, ce qui ne sera pas sans conséquences pour la conception des systèmes hybrides du futur.

## 1.5 Conclusion

Le programme expérimental décrit dans ce document a été conçu autour de l'installation WNR qui possède le flux de neutrons le plus intense dans la gamme d'énergie d'intérêt, et des systèmes de détection sophistiqués parfaitement adaptés à la mesure de rayonnement prompt de fission.

Les mesures de détection des rayons X et γ dans la fission de l'uranium 238 et 235 ont été réalisées sur GEANIE avec succès. Cela a nécessité une reconfiguration en profondeur du système de détection et d'acquisition. L'analyse détaillée des données récoltées pour l'extraction de la distribution en charge est en cours, et plusieurs publications techniques sont déjà parues.

Les mesures de neutrons prompts dans la fission de l'uranium 238 et 235 ont aussi été réalisées avec succès à l'aide de FIGARO. Les données finalisées, comparées aux calculs prédictifs réalisés à Los Alamos et à Bruyères-le-Châtel sont publiées. Dans le cadre de cette collaboration d'autres données seront prochainement disponibles: neptunium 237, plutonium 239 et thorium 232.

Dans ce document, on a aussi montré la nécessité de la mise au point de nouveaux détecteurs, illustrée par le travail sur les cellules solaires (chapitre 2.2 et 4). Cette activité ne doit pas être considérée comme régaliennne mais bien une fin pour la réalisation des expériences et l'obtention des résultats de physique.
# Chapitre 2

## Articles publiés

2.1 Nucl. Intrum. and Meth. A490: Mise au point du détecteur de fragments de fission transparent aux X pour GEANIE
A fission-fragment-sensitive target for X-ray spectroscopy in
neutron-induced fission

T. Ethvignot$^{a,*1}$, T. Granier$^a$, L. Giot$^a$, P. Casoli$^a$, R.O. Nelson$^b$

Received 29 April 2002; accepted 16 May 2002

Abstract

A fission-fragment-sensitive detector built for low-energy photon spectroscopy applications at the WNR “white” neutron source at Los Alamos is described. The detector consists of eight layers of thin photovoltaic cells, onto which 1 mg/cm² of pure ²³⁸U is deposited. The detector serves as an active target to select fission events from background and other reaction channels. The fairly small thickness of the detector with respect to transmission of 20–50 keV photons permits the measurement of prompt fission-fragment X-rays. Results with the GEANIE photon spectrometer are presented. © 2002 Elsevier Science B.V. All rights reserved.

Keywords: Fission-fragment detector; Photovoltaic cells; Solar cells; Neutron-induced fission

1. Introduction

In the fission of a heavy nucleus, both fragments
are formed with an excess of neutrons, excitation
energy and spin. The most efficient way for the
fragments to cool down is prompt neutron and
γ-ray emission. As the excitation energy decreases,
low-lying levels in the secondary fragments are
reached, and internal conversion becomes a
competitive means of releasing the remaining
excitation energy. In this process, the emitted K

electron leaves a vacancy that is promptly filled by
less bound electrons. The electronic cascade is
accompanied by emission of X-rays. The overall
timescale of the phenomenon was established to be
of the order of nanoseconds, and the average
number of K-X-rays emitted is ≈ 0.55 per fission
fragment [1]. The K-X-ray yield as a function of
mass and charge of the fragment was measured by
Reisdorf et al. [2] for different fissioning systems.
It was found that X-ray yields do not depend
much on the fissioning system, and that heavier
product nuclei produce more X-rays.

An active uranium target for the measurement
of K-X-rays from fission fragments is presented
in this article. The scientific goal is to extract
charge yields in fission induced by neutrons over a
broad range of energies. These data are of
importance for the fundamental understanding
of nuclear fission and have applications for the

<footnote>ª Service de Physique Nucleaire, Commissariat à l'Énergie Atomique, DAM Ile-de-France, BP 12, F-91680 Bruyères-le-Châtel, France</footnote>

<footnote><sup>b</sup>Los Alamos Neutron Science Center, MS H855, Los Alamos National Laboratory, NM 87545, USA</footnote>

<footnote>*Corresponding author. Tel.: +33-1-6926-6351; fax: +33-1-6926-7063.</footnote>

<footnote>E-mail address: thierry.ethvignot@cea.fr (T. Ethvignot).</footnote>

<footnote n="1">¹Partially supported by Délégation Générale pour l'Arme-
ment of the French Ministry of Defense.</footnote>
design of spallation-based systems, e.g. sub-critical
reactors.

## 2. Experimental setup

At the WNR intermediate energy neutron source, the germanium detector array GEANIE is used for various measurements [3]. Results on nuclear fission processes with <sup>235</sup>U [4] and <sup>238</sup>U [5] targets were recently published. Below 100 keV, the spectra obtained with passive uranium targets are dominated by background. For the study of fission X-rays, it was necessary to build an active target. The setup was designed to optimize the fission rate, the fission-fragment detection efficiency, and the X-ray transmission for fast coincidence measurements with GEANIE.

### 2.1. Photovoltaic cells

Siegert demonstrated 20 years ago that photovoltaic cells, or solar cells, could be used as fission-fragment detectors [6]. Solar cells main advantage with respect to standard solid-state detectors is their very low cost. They can be operated in open air, without light protection. With appropriate charge-sensitive preamplifiers, solar cells are essentially insensitive to γ-rays, neutrons and light charged particles, and can therefore be used in a hostile environment [7]. In the results reported in Ref. [8], it is mentioned that the solar cells can sustain very high doses of light charged particles without showing any deterioration in performance. However, we observed that solar cells locally suffer from intense irradiation damage with a <sup>252</sup>Cf source, with a typical efficiency half-life of 8 h for 10 μCi in close contact. This can be explained by the fact that the α particle density rate was much higher with our <sup>252</sup>Cf source than it was in the work of Ref. [8]. Solar cells have been employed as fission detectors in various applications: high-efficiency fission-fragment detectors for sub-barrier fission investigations [9]; fission trigger or veto for heavy-ion-induced fission and spontaneous fission spectroscopy with the EUROBALL γ-ray spectrometer [10]; high neutron flux counter at CERN [11];

Solar cells come in different sizes and thicknesses. It is easy to cut them in various shapes with a diamond head saw. For our purpose, we have used thin solar cells developed for space applications [12]. Their thickness is ≤140 μm, including ≈10 μm of silver backing.

### 2.2. Uranium deposits

In this work, several physical and chemical methods were used to deposit uranium on the photosensitive side of the cells. There are two advantages to do so: since fission fragments are emitted back-to-back, this is a most efficient way to detect fission; also, no support is needed for the target and therefore any quantity of actinide can be deposited on the cells. Deposits made from drying a uranium nitrate solution were not uniform. Electro-spraying and electro-deposition methods gave better results. However, the deposit did not always stick well. The best results were obtained with the SIDONIE mass separator at CSNSM/Orsay [13]. Pure <sup>238</sup>U was separated from the other isotopes and deposited on the cells. A thickness of 1 mg/cm² was chosen: this thickness is <50% of the range of most fission fragments in uranium on the one hand, but it is big enough to yield a reasonable fission rate on the other hand. A 50 Å carbon layer coated the uranium deposits to reduce potential oxidation and contamination.

### 2.3. Mounting

A diagram representing the setup is shown in Fig. 1. The setup is designed to detect one fragment per fission in order to minimize the amount of material in the neutron beam. Copper ring collectors are mounted on both sides of each cell. The back sides of the cells are grounded together. Each “sandwich” is isolated with plastic rings, and has a typical thickness of 3 mm. The eight sandwiches are mounted in a plastic holder not represented in the picture. Only the cells and the deposits “see” the neutron beam. The total amount of material was minimized in order to maximize X-ray transmission from the uranium
<figure><img src="image_3.png" /></figure>

Fig. 1. Sketch of the fission-fragment-sensitive target. The cell dimensions are 2.5 × 2 cm (with a thickness of 0.014 cm exaggerated on the sketch), the deposit dimensions are 2 × 1.8 cm. Neither the plastic mount holding the sandwiches together, nor the GEANIE photon spectrometer surrounding the target are represented in the diagram.

deposits to the GEANIE photon detectors surrounding the target.

## 2.4. Electronics

Special charge-sensitive preamplifiers were designed and built at CEA/Saclay [14]. No high voltage bias is applied to the solar cells. The pulse height for fission fragments depends on the size and thickness of the cell, but is typically 50 mV. The rise time is 50 ns and the decay time is several hundreds of ns. The noise is white and has a typical maximum of 10–20 mV. Special care is taken about electrical grounding and shielding of the setup. As shown in Fig. 1, preamplifier coaxial cable shields are grounded together as close as possible to the cells. This permits stacking cells very close to one another and reduces noise pickup. Preamplifier outputs are simply split with a coaxial “T”. Standard timing filter amplifiers (20 ns integration and 20 ns differentiation) and leading edge discriminators are utilized to generate a timing logic pulse. Linear amplifiers are utilized to generate the energy pulses. FERA time-to-digital and analog-to-digital converters are used for time and energy digitization in the GEANIE data acquisition system. The solar cell logic pulses also provide a trigger of valid events in order to

single out fission X- and γ-rays detected with the GEANIE photon detectors from the large background.

# 3. Results and discussion

## 3.1. Time resolution

The time resolution has a ≈10 ns FWHM. It was measured with the time-of-flight gaussian distribution of γ-ray induced fission at WNR as shown in Fig. 2.

## 3.2. Energy dispersion

The energy spectrum is used to discriminate low-energy background counts from higher-energy fission-fragment pulses. These two groups of counts are well separated, although one expects a continuous fragment energy distribution of slow fragments. It is worth noting that with 1 mg/cm² (resp. 0.3 mg/cm²) deposits, the average fragment energy is 3% (resp. 10%) higher with the deposit upstream vs. downstream. This is understood as a consequence of the linear momentum transfer in high-energy neutron-induced fission reactions.

In order to understand the energy distribution of the measured spectrum, we have performed a simple Monte-Carlo simulation of the energy response of the cell-deposit system at 14 MeV. Initial mass and charge distributions of the fission of ²³⁸U and prompt neutron multiplicity were taken from evaluated data [15]. The total kinetic energy of the secondary fragments was deduced from the Viola systematics prescription for the primary fragments [16]. The energy loss of the secondary fragments in the deposit was computed with the STOP algorithm of the TRIM package [17]. An energy resolution of 20% was used for the calculations. Finally, the pulse height defect of the cells was taken from Ref. [14]. The result of the simulation with a 1 mg/cm² deposit are compared with the experimental spectrum in Fig. 3. One can see that there is an experimental threshold of ≈30 MeV, accounting for an efficiency loss of ≈16%. Above 30 MeV, the calculated final distribution reasonably matches
<figure><img src="image_4.png" /><figcaption>Fig. 2. Time-of-flight spectrum for neutron induced fission detected in one solar cell (1 mg/cm² ²³⁸U deposit). The detector was positioned 20.3 m away from the production target. The WNR proton beam micro-pulse spacing was set to 1.8 µs. The small peak at ≈68 ns represents γ-ray induced fission. Its width is used to measure the time resolution of the detector. The lack of counts between 1240 and 1300 ns is due to dead time in the timing electronics that can be fixed with further adjustments.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3. Comparison of the kinetic energy spectrum of the fragments detected with the setup in the fission of ²³⁸U with 14 MeV neutrons (1 mg/cm² ²³⁸U deposit). The calculated initial distribution before energy loss in the deposit for all final energies (resp. for final energies > 30 MeV) is represented with the dashed (resp. continuous) histogram. The closed squares represent the calculated final energy distribution. The experimental distribution, plotted with open circles, was obtained for neutron energies between 12 and 16 MeV at WNR.</figcaption></figure>
the experimental data. Comparing the symmetric initial distributions for all detected fragments and for detected fragments with a final energy > 30 MeV, one can see that the slowest fragments are more affected by the experimental threshold. This 10% bias on the detected fragment distribution asymmetry will have to be taken into account for the X-ray yield of the heavy (slow) fragments.

### 3.3. Detection efficiency

The time-of-flight spectrum was converted into neutron energy in order to compare the response of one solar cell with a well-calibrated fission chamber containing 0.4 mg/cm² of pure $^{238}$U [18]. The ratio of the number of fissions in the cell and in the chamber gives the cell efficiency at all WNR energies. The plots are shown in Fig. 4. Both detectors had their deposits downstream. The neutron beam collimation was smaller than the deposits, i.e. 1.3 cm in diameter. A factor 2.5 was applied to compensate for the smaller thickness of the uranium layer. One can see that the cell efficiency is roughly constant over the whole energy range. Assuming a 100% efficiency for the fission chamber, the absolute efficiency for the

cells is here estimated to be about 65%. This figure is in approximate agreement with calculations at 14 MeV described in the previous subsection. Indeed, it was calculated that 6% of the fragments do not deposit any energy in the solar cell, i.e. they are not detected. Another 16% of the fragments deposit <30 MeV. The silver strip collectors on the top of the cells, onto which uranium is also deposited, and the titanium oxide reflector were not modeled but they could account for a loss of a few percent of the detector efficiency. Additional measurements performed with thicker solar cells gave somewhat lower efficiencies. In that case, the losses might be due to the physical properties of the cells, i.e. broader silver strips and thicker reflector.

### 3.4. Fission and X-ray rates

With a 1.9 cm diameter neutron beam collimation and a 5 µA WNR proton beam intensity, a fission rate of $30 \text{ s}^{-1}$ was obtained at the GEANIE target position with seven working solar cells each with a 1 mg/cm² $^{238}$U deposit. Prompt X-rays, in a time coincidence gate of 200 ns, were detected with five Compton-suppressed low energy photon

<figure><img src="image_6.png" /><figcaption>Fig. 4. Comparison of the efficiency of a uranium coated solar cell to a reference fission chamber. In the upper plot, the number of fission events recorded during the same run are compared. A thickness factor (2.5) is applied to calculate the cell efficiency with respect to the fission chamber in the lower plot. Statistical error bars, not plotted, range from 3% at 1 MeV to 30% at 100 MeV.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Fig. 5. X-ray spectrum obtained with five GEANIE LEPS detectors. The data were fitted with seven Gaussians with quadratic background. The average energies obtained from each peak are indicated by a vertical line and the corresponding element name. The fission events were triggered with the fragment-sensitive target.</figcaption></figure>

spectrometers (LEPS) of the GEANIE array
mounted at about 10 cm from the active target.
With 10 days of beam time, thousands of counts in
X-ray lines from Iodine to Praseodymium were
acquired for the first time at a “white” neutron
source (see Fig. 5). These X-rays were not ob-
served in previous experiments with passive targets
because of the high in-beam background level in
the LEPS detectors below 100 keV.

**4. Conclusion**

A novel active target was designed and built to
perform fission fragment X-ray detection at a
white neutron source. The target consists of a
stack of eight solar cells coated with uranium
layers. The time resolution is <10 ns and permits
prompt X-ray detection in coincidence with
GEANIE's LEPS. An energy threshold of about
30 MeV for the detected fragments was deduced
when comparing energy spectra with simple
Monte-Carlo simulations. This introduces a small
bias on the mass distribution of the detected
fragments, i.e. the heavy fragment yield is ≈10%
lower than the light fragment yield. The efficiency
of the setup (≈65%, which is consistent with
calculations) was measured with comparison to a

reference fission chamber. With the active target,
X-ray yields in the fission of $^{238}$U were measured,
for the first time at a white neutron source, for
elements from Iodine to Praseodymium. Targets
with other actinides are being made. Fission yields
will be extracted from the data.

**References**

[1] R. Vandenbosch, J.R. Huizenga, Nuclear Fission, Academic Press, New York, London, 1973 and references therein.

[2] W. Reisdorf, et al., Nucl. Phys. A 177 (1971) 337.

[3] J.A. Becker, R.O. Nelson, Nucl. Phys. News Int. 7 (1997) 11; R.O. Nelson, et al., GEANIE at WNR/LANSCE a new instrument for neutron science, Proceedings of the International Conference on Nuclear Data for Science and Technology, Trieste, Italy, Italian Physical Society Conference Proceedings, Vol. 59, 1997, p. 445.

[4] W. Younes, J.A. Becker, L.A. Bernstein, P.E. Garrett, C.A. McGrath, D.P. McNabb, R.O. Nelson, G.D. Johns, W.S. Wilburn, D.M. Drake, Phys. Rev. C 6405 (2001) 4613.

[5] Th. Ethvignot, Th. Granier, P. Casoli, R.O. Nelson, M. Devlin, N. Fotiades, G.D. Johns, P.E. Garrett, W. Younes, J.A. Becker, L.A. Bernstein, C.C. McGrath, Intermediate energy neutron-induced fission of uranium: product yields and isomer studies, Proceedings of the International Nuclear Conference on Nuclear Data for
Science and Technology at Tsukuba, Japan, October 2001, J. Nucl. Sci. Tech., in press, 2002.

[6] G. Siegert, Nucl. Instr. and Meth. 164 (1979) 437.

[7] E. Liatard, S. Akrouf, J.F. Bruandet, A. Fontenille, F. Glasser, P. Stassi, Tscan Ung Chan, Nucl. Instr. and Meth. A 267 (1988) 231.

[8] N.N. Ajitanand, R.P. Anand, S.R.S. Murthy, K.N. Iyengar, Nucl. Instr. and Meth. A 300 (1991) 354.

[9] N.N. Ajitanand, A. Narayanan, T. Ethvignot, H. Yu, J.M. Alexander, B. Lund, M. Gai, Nucl. Instr. and Meth. A 320 (1992) 596.

[10] R. Lucas, et al., Study of fission fragments from $^{12}$C+$^{238}$U reactions: prompt and delayed spectroscopy, Proceedings of the International Conference on Fission and Neutron-Rich Nuclei, St. Andrews, UK, 28 June–2 July 1999, World Scientific, Singapore.

[11] S. Andriamonje, et al., Phys. Lett. B 348 (1995) 697.

[12] The thin space solar cells were purchased from Solar World (www.solar-world.com).

[13] R. Meunier, J. Camplan, J.L. Bonneval, J.L. Dabanhaurou, D. Deboffle, P. Leclercq, M. Ligonniere, P. Moroy, Nucl. Instr. and Meth. 139 (1976) 101.

[14] C.H. Theisen, et al., SAPHIR: a fission-fragments detector, in: G. Fioni (Ed.), Proceedings of the Second International Workshop on Nuclear Fission and Fission-Product Spectroscopy, Seyssins, France, 22–25 April 1998, AIP, New York, NY, 1998, pp. 143–150.

[15] A. Wahl, Contribution to Compilation and Evaluation of Fission Yield Nuclear Data, IAEA-TECDOC-1168, 2000, p. 58.

[16] V.E. Viola, K. Kwiatkowski, M. Walker, Phys. Rev. C 31 (1985) 1550.

[17] J.F. Ziegler, The Stopping and Range of Ions in Solids, Pergamon Press, New York, 1985.

[18] S.A. Wender, S. Balestrini, A. Brown, R.C. Haight, C.M. Laymon, T.M. Lee, P.W. Lisowski, W. McCorkle, R.O. Nelson, W. Parker, N.W. Hill, Nucl. Instr. and Meth. A 336 (1993) 226.
2.2 Nucl. Intrum. and Meth. A554: Technique de la compensation appliquée aux cellules solaires en milieu hautement ionisant
<figure><img src="image_8.png" /></figure>

ELSEVIER

Available online at www.sciencedirect.com

SCIENCE @ DIRECT®

Nuclear Instruments and Methods in Physics Research A 554 (2005) 340–346

NUCLEAR
INSTRUMENTS
& METHODS
IN PHYSICS
RESEARCH

Section A

www.elsevier.com/locate/nima

# A compensated fission detector based on photovoltaic cells

M. Petitª, T. Ethvignotª, T. Granierª,*, R.C. Haightᵇ, J.M. O'Donnellᵇ,
D. Rochmanᵇ,<fnref n="1" />, S.A. Wenderᵇ, E.M. Bondᶜ, T.A. Bredewegᶜ, D.J. Vieiraᶜ,
J.B. Wilhelmyᶜ, Y. Danonᵈ

Received 27 May 2005; received in revised form 29 July 2005; accepted 28 August 2005

Available online 16 September 2005

## Abstract

Standard techniques of event-by-event detection of fission may fail when operated in high γ-ray or particle radiation environments. This is the case within the 800 MeV proton-driven lead slowing-down neutron spectrometer at LANSCE where standard fission detectors are found to be inoperable for microseconds to milliseconds after each proton pulse. To overcome this problem, a simple fission fragment detector based on compensated photovoltaic cells has been developed. The compensated detector has lower susceptibility to the strong γ-flash and can recover much faster than an uncompensated detector. This detector is well adapted to applications involving the detection of fission in regions where high intensity γ-ray and/or particle radiation fields exist.

© 2005 Elsevier B.V. All rights reserved.

Keywords: Fission; Fission detection; Compensated detector; Lead slowing-down spectrometer; Photovoltaic cells

## 1. Introduction

A lead slowing-down spectrometer (LSDS) has been recently implemented on the 800 MeV proton

beam line of the Los Alamos Neutron Science Center (LANSCE) with the ultimate goal of measuring the neutron-induced fission cross-section of the first metastable state of uranium 235 (²³⁵M U, 77 eV) in the 1 eV–100 keV region [1]. This unprecedented measurement will provide new constraints to the nuclear reaction models which predict substantial differences between the isomer and the ground state cross-sections. Indeed, in this energy domain, one expects a cross-section up to

<footnote>ªCEA/DAM Ile-de-France, DPTA/Service de Physique Nucléaire, BP 12, 91680 Bruyères-le-Châtel, France</footnote>

<footnote>ᵇLANSCE-3, Los Alamos National Laboratory, MS H855, Los Alamos, NM 87545, USA</footnote>

<footnote>ᶜC-INC, Los Alamos National Laboratory, MS J514, Los Alamos, NM 87545, USA</footnote>

<footnote>ᵈRensselaer Polytechnic Institute, Troy, NY 12180, USA</footnote>

<footnote>*Corresponding author. Tel.: +33 1 6926 5786; fax: +33 1 6926 7663.</footnote>

<footnote>E-mail address: thierry.granier@cea.fr (T. Granier).</footnote>

<footnote n="1">¹Present address: National Nuclear Data Center, Brookhaven National Laboratory, Upton, NY 11973-5000, USA.</footnote>
40% smaller for the excited state [2,3] whereas at thermal energy previous measurements have reported an isomeric cross-section that is twice as large as that for the ground state [4–6].

Since the half-life of $^{235m}$U is relatively short (26 min), only small samples, i.e. ~10 nanograms, will be available. To compensate for the limitation in count rate, the main advantage of the new proton-driven lead spectrometer is to provide an intense neutron flux in the 1 eV–100-keV region. The instrument consists of a 20 metric tonne cubic lead assembly to the center of which the LANSCE proton storage ring 800 MeV proton beam is transported and stopped in a tungsten target. The proton beam is emitted within short pulses (typically <200 ns) and induces spallation reactions in the tungsten target. Most of the neutrons resulting from these reactions slow down through multiple, quasi-isotropic elastic scattering in the lead assembly from the MeV region down to the thermal regime, giving the system its properties of spectrometry and high neutron intensity [7]. Detailed descriptions of the instrument’s characteristics and the experimental program are given in Ref. [1] as well as references of previous works that have lead to this established technique.

To perform the detection and counting of fission, thin photovoltaic cells (often referred to as solar cells) used as fission fragment detectors are one of the options followed in our experimental program. These detectors are compact, rugged and inexpensive and they have a high efficiency (see e.g. Refs. [8,9]). Nevertheless, with increasing proton pulse power in the LSDS, solar cells as well as other classical detectors (i.e., ionization chambers, surface barrier junctions, scintillators, etc.) are subject to oscillation and saturation due to the interaction with the intense high energy particles and prompt γ-rays accompanying the spallation reactions (γ-flash). This results in a dead time after each proton pulse and this makes detection of fission very difficult or impossible. Indeed, the net effect is a loss of fission events affecting the higher energy part of the neutron spectrum which corresponds to the shorter time-of-flight. This problem required implementing a compensated detector system similarly to what is

classically done with ionization chambers used in high γ-ray fluxes.

## 2. Solar cells as fission detectors in a LSDS

The use of solar cells as fission fragment detectors is a well-known technique in experimental nuclear physics (see for example Refs. [10,11]).

In our experimental program we aim at measuring the fission cross-section of $^{235m}$U and other rare isotopes relative to $^{235}$U. The absolute determination of the detection efficiency is thus not required. In this framework, photovoltaic cells offer several advantages. They can operate in open air and are quite insensitive to radiation damage. Their mass is relatively small and therefore, they induce minimal perturbations on the neutron flux. Also, as they do not require vacuum pumping, so operations with fissile samples are more rapid and convenient than with the usual ionization fission chambers. This point is particularly important in the case of short-lived nuclei such as $^{235m}$U.

The thin (~140 µm, solar cells used in this work were developed for the space industry [12]. They are 2 × 2 cm² Si junctions with one side covered with a silver backing. Their full characteristics as fission fragment detectors (i.e. timing, detection efficiency, Schmitt parameters, etc.) are summarized in Ref. [8].

For the tests in the LSDS, we used long-lived fissionable material such as $^{235}$U and $^{239}$Pu. The samples were deposited directly onto the active surface by electrodeposition. Alternatively, they can be deposited on a separate substrate and brought next to the detector for fission counting.

The cells are operated with the “SAPhIR” preamplifier that were specially developed with surface mounted component technology for use with photovoltaic cells used as fission detectors [13]. This preamplifier is adapted to the cells’ large intrinsic capacity (several nF/cm²). The output voltage is linearly proportional to the input current. The fast intrinsic rise time (~10 ns) is therefore preserved. The typical pulse height for fission fragments is 50 mV with 10 mV of white noise (for a 2 × 2 cm² cell). The decay time constant is about 500 ns.
In this work, the fission cross section measurements solely require timing information from the fission pulses out of the preamplifier. Discrimination from noise was achieved either with classical electronics (fast filter amplifier and constant fraction discriminator) or through digital filtering algorithms (see Ref. [14]).

### 3. γ-Flash saturation

The γ-flash effect is strongly correlated with the number of protons per beam pulse. The experiments with $^{235m}$U will necessitate a proton integrated intensity of 1 µA. With the usual proton storage ring (PSR) repetition rate of 20 Hz, this corresponds to proton pulses of 50 nC integrated charge. However, ongoing developments will allow the PSR to be operated at 30 Hz and possibly at 40 Hz allowing to lower the beam pulse size to respectively 33 and 25 nC/pulse. In practice, the γ-flash effect depends also on the position within the lead assembly. We observed that the effect decreases when the distance to the target is increased. Also, it is more pronounced in the downstream part of the assembly.

Typical waveforms exhibiting ringing and saturation are plotted in Fig. 1 for three different sizes of the proton pulses. They correspond to the voltage output of the preamplifier recorded after the proton pulse (at $t=0$). The detector was located at a distance of ~60 cm from the center of the assembly. In each case, shortly after the proton pulse, one can observe a high amplitude signal attributed to the γ-flash (1). This signal is followed in Fig. 1(a) and (b) by a ringing with ~25 µs period (2). Only the positive excursions are visible since the preamplifier output saturates at negative values (~ -90 mV with a 1 MΩ impedance). The same ringing also exists for higher numbers of protons per pulse (Fig. 1(c)), but it is preceded by a long negative period of saturation (7). The total duration of the saturation and ringing can reach several milliseconds depending on the number of protons in the beam pulse. It is then followed by a return to the baseline (3). Fission signals are visible (arrows) on top of the γ-flash signal and after the ringing (4). They are also observed on top of the

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 1. Waveforms (output voltage as a function of time) recorded after one proton pulse with a $^{235}$U coated solar cell (without compensation) in the LSDS, for 3 different proton pulse sizes: 5 nC (a), 8 nC (b) and 15 nC (c). Time 0 corresponds to the incident proton pulse. Fission signals are indicated by arrows (see text for additional discussion).</figcaption></figure>

ringing (6) and in the saturation region between two positive excursions (5). In these cases there is no time dependent inefficiency in the detection of fission provided that the subsequent signal processing is able to discriminate the fission signals [14].
However, in the case of Fig. 1(c), no fission is observed in the first saturation period (7), i.e. for 80 µs after the beam pulse emission. This corresponds to neutron energies higher than ~25 eV. Thus, for 15 nC proton pulses no cross-section measurement is possible above ~25 eV no matter of the level of performance of signal processing. Tests at higher proton pulse intensity confirm the irreversible loss of the fission events for even larger periods after the proton pulse, i.e. at lower neutron energy.

In order to extend the range of fission detection up to 100 keV, one must be able to recover from the saturation in less than a microsecond. For this purpose, a method of γ-compensation for solar cells was developed similarly to the 50-year-old technique of γ-compensated ionization chambers [15,16]. The technique was tested at ELSA, a pulsed γ-ray source facility at Bruyères-le-Châtel [17,18] and directly within the LSDS at LANSCE.

## 4. γ compensation with solar cells

The compensation principle proposed here is based on two identical solar cells that are connected together so that their current outputs are opposite. One of the cells is exposed to the fissile sample and is used as a fission fragment detector. The other cell is not exposed to the fission source and serves as a compensator. As both cells experience the same γ-flash, γ-flash-induced signals compensate whereas the fission signals are preserved. Two basic diagrams follow this principle with the cells connected either in antiparallel or in antiseries. In this work the antiparallel connection was used. The compensated setup is sketched in Fig. 2. Although this connection alters slightly the signal to noise ratio with the Saphir preamplifier, it was checked with a spontaneous fission source ($^{252}$Cf) that the detection efficiency, timing and response linearity were preserved.

In order to test the response of the compensated setup to a γ-flash, photon irradiations have been performed at the ELSA facility. The photon beams were produced by Bremmstrahlung by bombarding a 1.2 mm Ta converter with a

<figure><img src="image_12.png" /><figcaption>Fig. 2. Diagram of the compensated fission detector. The cells are connected in antiparallel order to compensate (by subtraction) the signals induced by the γ-flash.</figcaption></figure>

15 MeV electron beam. The electron pulses were Gaussian (150 ns FWHM) and were delivered at a 10 Hz repetition rate. The solar cell setup was placed 150 cm downstream to the target. No fissionable samples were used in these tests. Fig. 3 represents the setup response with and without compensation. The number of beam electrons per pulse was increased by a factor of four for the experiment with compensation in order to evaluate the effect with greater sensitivity. Thus an attenuation by a factor of 20 is observed on the γ-flash-induced signal with this simple compensation system. This prevents the preamplifier from saturating and oscillating.

The compensated setup has also been tested in the LSDS with fissionable samples. Similar compensation performance was obtained, i.e. reduction of the γ-flash signal over the whole time range. This is illustrated at Fig. 4 where a waveform obtained with a 40 nC proton pulse is displayed. One can note that the amplitude of the excursions near $t = 0$ are largely reduced compared to Fig. 1(c). Also, no saturation is observed and the fission signals are easily distinguished on top of the distorted base line. The fission signals were discriminated online through signal processing and we were able to achieve satisfactory measurements of standard cross sections up to neutron energies of 50 keV (i.e. down to ~1.5 µs after the proton pulse) with 40 nC proton pulses.
<figure><img src="image_13.png" /><figcaption>Fig. 3. Response to a γ-flash (at $t=0$) with (full line) and without (dashed line) compensation (identical cells, no fissionable material). Note that the electron beam intensity was larger by a factor of 4 in the case of compensated setup: 0.18 vs. 0.045 nC/pulse. Therefore, the compensation reduced the γ-flash peak by a factor of 20.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 4. Waveform obtained in the LSDS with the compensated setup in the case of a 40 nC proton pulse (preamplifier output). The amplitude of the excursions near $t=0$ is drastically reduced compared to Fig. 1(c) and fission signals are observed.</figcaption></figure>

## 5. Investigations towards a refined compensation

Small compensation defects may remain however, due to small differences in the cells' suscept-

<figure><img src="image_15.png" /><figcaption>Fig. 5. Diagram of a refined compensation system. A potentiometer *R* is inserted between the two cells.</figcaption></figure>

ibility. The compensation level can be improved by adjusting the cells response to the γ-flash until they match and cancel precisely. This can be obtained through a divider bridge with a variable potentiometer such as in the diagram represented in Fig. 5. With this diagram, a compensation refinement is possible only if the intrinsic sensitivity of the compensating cell is slightly higher than the sensitivity of the compensated cell. This can be obtained by reducing the size of the compensating cell (by cutting out a small fraction of it) which then gets a smaller capacitance. Then the refined compensation is reached by adjusting the potentiometer. Fig. 6 represents output signals obtained at ELSA with the compensated setup for four different values of the potentiometer (0, 20, 50 and 325Ω) in response to equivalents γ-flashes. The best compensation was obtained for a 20Ω resistance. For a null resistance, i.e. no divider bridge, the resulting signal was found negative due to the slightly larger intrinsic sensitivity of the compensating cell. In the future, this system will be equipped with a motorized potentiometer so that the compensation level may be remotely optimized.

## 6. Conclusion

A compensated fission detector based on photo-voltaic cells has been designed for operation at the 800 MeV proton-driven lead slowing-down
<figure><img src="image_16.png" /><figcaption>Fig. 6. Response of the compensated solar cell to the same γ-flash with four different values of the potentiometer. In order to perform a fine adjustment, the compensating cell had a slightly higher gain than the compensated cell. Therefore, the signal is negative for $R = 0 \Omega$.</figcaption></figure>

spectrometer at LANSCE. The detector is designed so that the γ-flash induced signal is dramatically reduced before preamplification. We have demonstrated this method with success in the LSDS for proton intensities up to 40 nC/pulse which is above the beam pulse size required for the future experiments with 1 μA proton integrated intensity and 30 Hz repetition rate. Investigations are in progress to extend this domain of operation to larger beam pulse sizes in the near future. They focus on compensation refinement, preamplifier optimization and wave-form digital filtering.

This detector should also be useful for other applications, in particular where the detection of fission within high radiation environments is involved.

## References

[1] D. Rochman, R.C. Haight, J.M. O'Donnell, A. Michaudon, D.J. Vieira, E.M. Bond, T.A. Bredeweg, A. Kronenberg, J.B. Wilhelmy, T. Ethvignot, T. Granier, M. Petit, Y. Danon, Nucl. Instr. and Meth. A (2005), accepted for publication.

[2] J.E. Lynn, A.C. Hayes, Phys. Rev. C 67 (2003) 014607.

[3] W. Younes, H.C. Britt, Phys. Rev. C 68 (2003) 034610.

[4] V.I. Mostovoi, G.I. Ustroyev, At. En. 5 (1964) 241.

[5] W. Talbert, et al., Phys. Rev. C 36 (1987) 1896.

[6] A. D'Eer, et al., Phys. Rev. C 38 (1988) 1270.

[7] T. Granier, L. Pangault, T. Ethvignot, R.C. Haight, X. Ledoux, V. Méot, Y. Patin, P. Pras, M. Szmigiel, R.S. Rundberg, J.B. Wihelmy, Nucl. Instr. and Meth. A 506 (2003) 149.

[8] T. Ethvignot, T. Granier, L. Giot, P. Casoli, R.N. Nelson, Nucl. Instr. and Meth. A 490/3 (2002) 559.

[9] M. Petit, Thèse de doctorat, Université de Bordeaux, France, 2002.
[10] G. Siegert, Nucl. Instr. and Meth. A 164 (1979) 437.

[11] E. Liatard, et al., Nucl. Instr. and Meth. A 267 (1988) 231.

[12] The thin solar cells were purchased from Solar World (http:www.solar-world.com).

[13] C.H. Theisen, et al., A fission-fragments detector, in: Proceedings of the Second International Workshop on Nuclear Fission and Fission-Product Spectroscopy, Séys-sins, France, 22–25 April 1998, AIP, New York, NY, 1998, p. 143.

[14] K.D. Huff, Digital filtering applications to the lead slowing-down spectrometer, Los Alamos National Laboratory Report LA-UR-04-8757, 2004.

[15] D.H. Wilkinson, Ionization Chambers and Counters, Cambridge University Press, Cambridge, 1950.

[16] P.E. Koehler, J.A. Harvey, N.W. Hill, Nucl. Instr. and Meth. A 361 (1995) 270.

[17] J.-G. Marmouget, A. Binet, Ph. Guimbal, J.-L. Coacolo, Present performance of the low-emittance, high-bunch charge ELSA photo-injected Linac, in: EPAC’02 Proceedings, Paris, 2002, p. 1795, http://accelconf.web.cern.ch/Accelconf/e02.

[18] Ph. Guimbal, et al., Status of the ELSA-2 project, in: EPAC’02 Proceedings, Paris, 2002, p. 1768, http://accelconf.web.cern.ch/Accelconf/e02.
2.3 Pont d'Oye V: Résultats des mesures des dis-tributions en charge et en masse avec GEA-NIE
Seminar on
# FISSION

Pont d'Oye V

<figure><img src="image_17.png" /></figure>

Editors: Cyriel Wagemans, Jan Wagemans & Pierre D'hondt

World Scientific
# STUDY OF THE MASS AND CHARGE DISTRIBUTION OF FRAGMENTS FROM FISSION INDUCED BY INTERMEDIATE ENERGY NEUTRONS ON URANIUM 238

P. CASOLI, T. ETHVIGNOT AND T. GRANIER

Commissariat à l'Energie Atomique,
Département de Physique Théorique et Appliquée,
Service de Physique Nucléaire,
B.P. 12, 91680 Bruyères-le Châtel, France
E-mail: pierre.casoli@cea.fr

R. O. NELSON, N. FOTIADES, M. DEVLIN AND D. DRAKE

LANSCE-3, MS H855,
Los Alamos National Laboratory,
Los Alamos, NM 87545, USA
E-mail: rnelson@lanl.gov

W. YOUNES, P. E. GARRETT AND J. A. BECKER

P.O. Box 808,
Lawrence Livermore National Laboratory,
Livermore, CA 94551, USA
E-mail: younes@llnl.gov

Prompt gamma-ray and x-ray spectroscopy techniques are being employed to study fission induced on $^{238}$U targets by neutrons of energy from 1 MeV to 150 MeV. Data are acquired using the GEANIE high resolution gamma-ray spectrometer at the LANSCE/WNR unmoderated spallation neutron source. Information on the pre-decay yields (excitation functions and isotopic distributions) were extracted from gamma and gamma-gamma coincidence data for a wide range of nucleides. Charge yields were extracted by measuring prompt x-rays from a thin, fission-sensitive target using photovoltaic cells specially designed. The experimental results are presented and compared to model calculations.

## 1. Introduction

Fragment production yields from neutron-induced fission of actinides have been extensively studied using gamma-ray spectroscopy for many years. In particular it is well known that, for uranium isotopes, production yields
increase with the neutron energy in the symmetric fission region¹.

These measurements have mostly been conducted at incident-neutron energies below 15 MeV due to limitations of neutron sources. The majority of neutron-induced fission data comes from thermal neutrons, reactor fast-neutron spectra, 14-MeV neutrons, and some data taken with monoenergetic neutron sources typically below 10 MeV. Above 15 MeV, very few measurements have been made².

There is now renewed interest in neutron induced fission, in particular at intermediate energies (i.e. between 14 MeV and 1 GeV) due to the potential use of high-energy accelerators for nuclear waste transmutation and energy generation, for the production of beams of rare and radioactive ions, to test models of fission using the increased computational power available, and to learn more about the details of the fission process.

In this perspective, a collaborative experimental program has been carried out by Bruyères-le-Châtel and Los Alamos. This program takes advantage of the WNR facility⁴ at LANSCE (Los Alamos Neutron Science Center), a spallation source which provides a relatively large flux of fast neutrons in a broad energy range extending up to more than 150 MeV.

Experiments utilizing the gamma-ray spectrometer GEANIE (GERmanium Array for Neutron-Induced Excitations)³ have provided new data on prompt gamma and x-ray emission.

The fission process is described as elongation of the nucleus followed by scission in which two neutron-rich primary fragments are emitted. These fragments rapidly emit neutrons after which we refer to them as secondary fragments. These are produced in excited states and two processes participate in their electro-magnetic de-excitation: gamma emission and internal conversion. The latter is accompanied by the emission of K x-rays characteristic of the fragment's atomic number.

About 10% of the isotopes observed in gamma decay are stable, while 90% undergo beta decay on a time scale of ms to 100's of seconds. It is the prompt gamma-rays emitted in less than 10 ns from the secondary fragments that are measured in our experiments. From the prompt gamma-ray yields we can infer fission secondary fragment yields for many product nuclides including the stable fragments that are not usually observed in radiochemical measurements of fission yields.

At incident-neutron energies above the neutron binding energy (about 6 MeV for actinides) one or more pre-fission neutrons may be emitted. Thus the observed yields at higher incident energies are summed over several fissioning system: $^{239}$U, $^{238}$U, $^{237}$U...
## Articles

In this report, we briefly describe the experiment and analysis, then results are presented for isotopic yield excitation functions, for the mass distribution of the barium isotopes and for inferred charge yields from the x-ray data.

## 2. Experiment

GEANIE is an array of 26 high-resolution germanium gamma-ray detectors. 11 of the detectors are LEPS dedicated to low energy photon spectroscopy, from 10 to 300 keV. The other 15 detectors are coaxial HPGe, more adapted to higher energy gamma-rays, typically from 300 to 2000 keV. BGO (bismuth germinate) background suppression shields are used on 20 of the detectors. GEANIE is located 20 meters from the WNR neutron production target at the end of a collimated flight path. The energies of the incident neutrons are determined by the time-of-flight technique, applied between the spallation target and GEANIE.

Two types of experiments were done at GEANIE with $^{238}$U.

The first one consisted of inclusive gamma-ray measurements and was performed with ~400 mg/cm$^2$ targets of $^{238}$U (99.8% enriched). GEANIE's many detectors gave the opportunity for analysis of the recorded gamma-rays in both single-gamma and double-gamma-gamma-coincidence modes. The target's relative thickness provided high gamma counting rates. However, the recorded gamma-rays originate not only from the fission fragments but also from other neutron-induced reactions occuring on the target or on the device, such as (n,n') or (n,xn) on uranium. Background due to neutron scattering is particularly high for low energy photons and fission K x-ray can not be seen.

For the x-ray measurements, it was necessary to detect the fission fragment in coincidence with the x-rays to get clean spectra in which the x-rays were observable. In a second class of experiment, we used solar cells as fission fragment detectors. We designed a thin, fission-sensitive target of $^{238}$U, consisting of eight 1 mg/cm$^2$-layers deposited onto eight photovoltaic cells$^5$. A coincidence with the detection of a fission fragment in a cell was required in the gamma and x-ray recording. Very thin solar cells were used to reduce x-ray attenuation. The active target was modeled with MCNP$^6$ to calculate the attenuation in the sample. The transmission average over the 8 cells ranged from about 15% for 10 keV x-rays (light fragments) to 70% for 35 keV x-rays (heavy fragments).
# 3. Analysis and Results

## 3.1. Identification of the fission fragments

Three different sets of data were used to identify the fission fragment: characteristic single-gamma-rays, gamma-gamma coincidences and fission-gamma coincidences. Thanks to a complementary analysis of the different types of measurement, we could identify about one hundred fission fragments. Elements from germanium to neodymium are seen. In some case up to ten isotopes of the same element are detected.

The total number of created fragments is estimated at about one thousand. The fragment production yields range over several order of magnitude with a maximum being about 4% of the total yield. The observed fission fragments represent also about 10% of the estimated total number of created fragments, but account for almost 90% of the total fission yield.

<figure><img src="image_18.png" /><figcaption>Figure 1. Pure neutron-induced fission prompt-gamma-ray spectrum obtained with a thin $^{238}$U target. All WNR neutron energies are included. A coincidence time of 50 ns between the fission fragment detectors and one of the 11 GEANIE LEPS was required.</figcaption></figure>

As a part of the analysis, the figure 1 shows a portion of a pure-fission spectrum obtained with a thin $^{238}$U target. All the gamma-rays are produced by fission fragments and most of the intense gamma-rays are labelled by the symbols of the atoms that emit them.
## 3.2. Excitation functions and isotopic distributions

For the extraction of the production cross sections of a fission fragment as a function of incident-neutron energy, i.e. the excitation function, the transitions of the ground state rotational band (GS) provide a good tool to study even-even nuclei. It is known that in these nuclei the decay will feed the low-spin transitions (almost 100% for the 2+ to 0+ transition). Measuring the intensity of a gamma-ray from a low spin transition gives a good measurement of the yield of the fragment which emitted it.

<figure><img src="image_19.png" /><figcaption>Figure 2. Excitation function of two GS transition of<sup>138</sup>Xe. Single and coincidence data are compared with Wahl systematics. Dotted lines indicate the error bars of the evaluations.</figcaption></figure>

As an example, figure 2 displays the excitation function of the lowest two GS transitions of <sup>138</sup>Xe and the measurement of the intensity of these two gamma-rays in coincidence. The three excitation functions are identical within errors, so we can assume that the gamma-rays are not contaminated: that means they are fed by the <sup>138</sup>Xe nucleus only, and that we can interpret these functions as production yields of the <sup>138</sup>Xe fragment.

The excitation functions show the thresholds corresponding to the different fission chances.

The data are compared to the Wahl systematics<sup>7</sup>. The systematics values are calculated from a multi-gaussian fit to mass and charge distributions of library data. The energy dependence is interpolated between data sets.
At energies above 14 MeV, Wahl used data from proton induced fission. The calculated values fit the data reasonably well.

This method allows determination of the excitation function for about 30 even-even fission fragments. In our data set, we see that the shapes of the functions are very different from one fragment to the other, especially concerning the height of the thresholds.

Then, we compare the production of different isotopes of the same element, obtaining isotopic distributions of the fragments.

<figure><img src="image_20.png" /><figcaption>Figure 3. Mass distribution of barium isotopes, measured for 3 incident energy bins and compared with the values from Wahl systematics at the average energies of the bins.</figcaption></figure>

As an example, figure 3 displays the production yields of five isotopes of barium, for three large incident-neutron energy bins. Results are compared with Wahl systematics. Both data and calculations show that at higher incident-neutron energies, the mean mass of the fragment goes down and the mass distribution is broader. Wahl calculations are consistent with our measurements at low incident energies but partially fail to reproduce them above 50 MeV.

### 3.3. Charge yields

Coincidences between photon and fission fragment detection in the active target experiment permitted prompt K x-ray measurements⁸. Due to the large number of K x-ray lines, five per element, the x-ray energy spectrum is quite complex. Nevertheless, it has been possible, within the limits of the
recorded statistics, to deconvolute the contribution of the different elements for several groups of incident-neutron energy. This was done by fitting the data with a multigaussian function with one free parameter per element (see figure 4). Background was considered linear on successive energy ranges.

<figure><img src="image_21.png" /><figcaption>Figure 4. Low energy photon spectrum for fission on <sup>238</sup>U induced by neutrons from 10 to 20 MeV. The 70 K x-ray lines correspond to 19 elements. The 15 most intense elements are labelled (K<sub>α</sub> peaks except silver's K<sub>β</sub>).</figcaption></figure>

In the seventies, Reisdorf and collaborators measured the x-ray yields per fragment in spontaneous and low energy neutron induced fission. It appears that this depends only weakly on the nature of the fissioning system. By applying Reisdorf's prescription to our x-ray yields, we extract an estimate of the charge distribution of the fission fragments. These distributions are displayed in figure 5 for four incident-neutron energy bins. These results exhibit the expected increase in the probability for symmetric fission as one goes toward high incident-neutron energies. The values of Wahl systematics are consistent with our data for all incident energies.

## 4. Conclusion

New data on prompt gamma and x-ray emission in intermediate energy neutron-induced fission on <sup>238</sup>U were obtained. Gamma-ray measurements have enabled the extraction of excitation functions for about 30 secondary fission fragments. An estimate of the charge distribution of the secondary fission fragments was obtained from x-ray measurements for several neutron-
<figure><img src="image_22.png" /><figcaption>Figure 5. Element yields per 100 fissions determined from the x-ray yield measurement for four incident-neutron energy bins (black dots): 1) threshold-6 MeV, 2) 11-20 MeV, 3) 20-50 MeV, 4) 50 MeV and up. Average energies are labelled. The histograms correspond to the Wahl systematics at the average energies.</figcaption></figure>

energy bins. The comparison of these results with evaluated data (Wahl systematics) shows that the evaluations are consistent with measurements below 20 MeV but partially fail to reproduce the data at higher energies.

References

1. S. Nagy et al, *Phys. Rev. C17*, 163 (1978).

2. C. M. Zöller et al, Seminar on fission "Pont d'Oye III", Habay-la-Neuve (Bel), Report EUR16295EN, 56 (1995).

3. P. W. Lisowski et al, *Nucl. Sci. Eng. 106*, 208 (1971).

4. J. A. Becker and R. O. Nelson, *Nucl. Phys. News Int. 7*, 11 (1997).

5. T. Ethvignot et al, *Nucl. Instrum. Meth. A 490*, 559 (2002).

6. J. Briesmeister, ed., "MCNP - A Monte-Carlo N-Particule Transport Code", LANL Report, LA-12625-M (1997).

7. A. C. Wahl, Systematics of fission-product yields, LANL Report, LA-13928 (2002).

8. T. Granier et al, preprint (2003).

9. W. Reisdorf et al, *Nucl. Phys. A 177*, 337 (1971).
## 2.4 Nucl. Intrum. and Meth. A523 : Mise au point du détecteur de neutrons de fission FIGARO
<figure><img src="image_23.png" /></figure>

ELSEVIER

Available online at www.sciencedirect.com

SCIENCE D DIRECT•

Nuclear Instruments and Methods in Physics Research A 523 (2004) 102–115

NUCLEAR
INSTRUMENTS
& METHODS
IN PHYSICS
RESEARCH

Section A

www.elsevier.com/locate/nima

# Neutron-induced reaction studies at FIGARO using a spallation source

D. Rochman<sup>a,*</sup>, R.C. Haight<sup>a</sup>, J.M. O' Donnell<sup>a</sup>, M. Devlin<sup>a</sup>, T. Ethvignot<sup>b</sup>, T. Granier<sup>b</sup>

Received 11 August 2003; received in revised form 8 December 2003; accepted 14 December 2003

## Abstract

A description is given of the new flexible facility Fast Neutron-Induced Gamma-Ray Observer (FIGARO) at the Los Alamos Neutron Science Center. FIGARO is designed to study fast-neutron-induced reactions that result in the emission of γ rays and neutrons, using the white neutron beam of the Weapons Neutron Research Facility. The emitted neutrons and γ rays are detected by several liquid scintillators and one high-resolution germanium or one barium-fluoride detector, respectively. As an example, the inelastic neutron scattering on Si from 4 to 20 MeV is presented and the results are compared with predictions of the nuclear model calculations performed with the codes GNASH and EMPIRE II.

© 2003 Elsevier B.V. All rights reserved.

PACS: 21.10.Ma; 25.40.Fq

Keywords: Neutron-induced reaction; FIGARO; White neutron source; Neutron inelastic scattering

## 1. Introduction

Inelastic neutron scattering with gamma-ray detection has been used in studies of nuclear structure and the reaction mechanism for many years. The data over a wide range of energies are also of great importance for applications. For example, in reactors, inelastic scattering is the

principal process for converting neutron energy into thermal energy. At higher energies, the design of accelerator-driven systems [1] requires these data for reliable of the neutron spectra, which in turn are the source terms for radiation damage and radiation transport in general.

Previous experimental studies have been carried out with two types of neutron sources: monoenergetic sources and continuous, or “white”, neutron sources. The former are traditionally carried out with Van de Graaf or cyclotron accelerators or d-T (14 MeV) sources. The latter have been pursued principally at electron linacs. For the monoenergetic sources, neutron emission spectra can be

<footnote><sup>a</sup> LANSCE-3, Los Alamos National Laboratory, MS H855, Los Alamos NM 87545, USA</footnote>

<footnote><sup>b</sup> CEA-DAM, BP 12, Bruyères-le-Châtel 91680, France</footnote>

<footnote>*Corresponding author.
E-mail addresses: rochman@lanl.gov (D. Rochman), haight@lanl.gov (R.C. Haight), odonnell@lanl.gov (J.M. O' Donnell), devlin@lanl.gov (M. Devlin), thierry.ethvignot@cea.fr (T. Ethvignot), thierry.granier@cea.fr (T. Granier),</footnote>
measured by time-of-flight (TOF) techniques. For “white” neutron sources, the elastically and inelastically scattered neutron spectra are usually obtained by unfolding the response of the neutron detector. Both approaches are limited. Our focus in this work is to measure the neutron-emission spectra from samples bombarded with a “white” source of neutrons from a spallation neutron source. The advantage of our “white” source over the monoenergetic neutron approach is that all incident neutron energies can be investigated from ~1 MeV to several hundred MeV. Truly mono-energetic neutron sources are only available up to 8 MeV and from ~13 to 17 MeV. The advantage over the previous work with electron-linac-based sources, which cover much of the same region, is that the intensity of our spallation source is higher, especially for incident neutrons about 5 MeV, and consequently a “double TOF” approach is possible.

The example we choose for the preliminary studies is neutron inelastic scattering on silicon. Data on this material are of great importance in applications, for it has been known for many years that neutron reactions on silicon are responsible for producing errors in computer memories [2]. The data are also very useful for testing nuclear reaction calculations because already many of the input parameters for these calculations are well known from other works [3–9]. The discrete states in $^{28}$Si are well known to rather high excitation energy [10]. Inelastic scattering data for the population of low-lying discrete states are available in the literature for incident neutrons from 2 to 6 MeV [11] and 6.8 to 12 MeV [12]. At 14.1 MeV, the full neutron-emission spectrum has been measured [13].

To realize the double TOF technique, we have developed the Fast neutron-Induced Gamma-Ray Observer (FIGARO) array of neutron and gamma-ray detectors. Initially, this capability was only to measure emitted gamma rays [14]. We realized that the addition of neutron detectors would make possible the measurement of neutron-emission spectra gated by specific gamma rays. This allows both the measurement of neutron-emission spectra if the subsequent gamma-ray cascade passes through the detected gamma ray. It also can allow measurement of the emitted neutron spectrum

gated by other specific gamma rays and thereby test model calculations with codes now under development, such as McGnash [15]. We describe here the array and present his capabilities with results from inelastic scattering on silicon. A preliminary report of the silicon data has been presented previously [16].

## 2. FIGARO facility

At the FIGARO facility, a well-collimated pulsed neutron beam is available. By taking advantage of the facility, we obtain neutron inelastic scattering data with good neutron energy resolution by the double (TOF) method. Data on neutron emission spectra from fast-neutron-induced fission were also obtained [17]. Typically, large amount of material (few grams) are needed for elastic or inelastic neutron-scattering studies to obtain relevant statistics and a good signal over background ratio.

### 2.1. Neutron source

Fig. 1 shows the layout of the Weapons Neutron Research (WNR) facility. A pulse of neutrons having a wide energy spectrum is produced in the Target-4 spallation neutron source at WNR by the interaction of a pulsed beam of 800 MeV protons from the Los Alamos Neutron Science Center (LANSCE) accelerator with a tungsten target [18]. The proton beam current is usually around 5 µA. The time structure of the proton beam is the following: one 650 µs-width macropulse every 8.3 ms made of 300 ps micropulses separated by 1.8 µs (see the insert in Fig. 1). The resulting neutron spectrum ranges in energy from a few keV to approximately the proton beam energy of 800 MeV, with most of the flux concentrated between 1 and 300 MeV.

Fig. 2, left, shows a typical neutron energy spectrum at 30° to the right of the proton beam (FIGARO flight path). The neutron production is monitored by a $^{235}$U and $^{238}$U fission chamber [19] placed at 16 m from the neutron production target. The energies of the incident neutrons are determined by a TOF method.
<figure><img src="image_24.png" /><figcaption>Fig. 1. Schematic view of the WNR facility with eight neutron flight paths. In the left insert, the proton beam structure is detailed.</figcaption></figure>

<figure><img src="image_25.png" /><figcaption>Fig. 2. Left: neutron fluence measured at the 30° right flight path in neutron/MeV/sr/micropulse. Right: picture of the neutron beam at the measurement location.</figcaption></figure>

## 2.2. *Experimental room*

Neutrons are delivered to the experimental room through the 30° right neutron flight path of the WNR facility [20]. The neutron beam is

collimated to a spot of 1.2 cm in diameter, according to the experiment requirement with iron and copper rings and with concrete blocks as shielding. By this arrangement, a well-collimated and a low-background neutron beam is obtained
in the experimental room. Fig. 2, right, shows the neutron beam profile at the measurement location. This picture of the beam was taken on a photographic film covered by a thin layer of polyethylene.

### 3. Design of experiment

#### 3.1. *Outline of the experimental method*

Fig. 3 shows the layout of the experiment. For the incident neutron energy calculation, the start of the TOF is given by the proton beam on the Target-4 and the TOF stop is obtained by the detection of a γ-ray from the neutron reaction on the target. The collimated-neutron beam hits a sample under study at 21 m from the Target-4, where nuclear excitations take place. The excited nuclei decay by the emission of γ-rays and neutrons, which are then detected.

#### 3.2. *Neutron and gamma-ray detection*

Neutron-energy spectra are measured using, at present, six liquid scintillation detectors EJ301 [21] (5 cm thick, and 12.5 cm in diameter of active scintillator), similar to NE213 [22,23]. These

scintillators exhibit excellent pulse-shape discrimination (PSD) properties, particularly for fast neutron counting and spectrometry in the presence of gamma radiation. The liquid scintillators are at about 1 m from the sample so that a second TOF can be used to determine the energy of the outgoing neutrons. The TOF start is given by the γ-ray detector and the TOF stop by the detection of the neutron in the liquid scintillator. By using a PSD technique with two gates (long and short) on the pulse height from the liquid scintillator signals, it is possible to separate the gamma-ray pulses from the neutron pulses. As the fraction of light appearing in the slow component depends on the nature of the excitation particle, the signals integrated with a short gate and a large gate are plotted with the short gate on the Y-axis and the long gate on the X-axis, see Fig. 4. The signals induced by gamma rays and by neutrons are then separated.

Fig. 5 presents two signals from the neutron detectors with and without PSD. On the left part, two peaks are clearly identified as the “gamma flash” from the spallation process when the protons hit the tungsten target and the neutrons $n'$ from the $(n, n')$ reactions. On the right part, only the neutron signal is conserved with the application of the PSD. Some background is still present.

<figure><img src="image_26.png" /><figcaption>Fig. 3. Experimental setup for neutron-inelastic scattering and fission-neutron emission measurements.</figcaption></figure>
Gamma rays, emitted from the decay of the excited nucleus are detected by one high-resolution Ge or one barium-fluoride (BaF₂) detector. The Ge detector provides a good timing signal, whereas the BaF₂ detector has a high gamma-ray efficiency and present a low neutron-capture cross-section. An energy window can be applied on the gamma-ray energy in order to select the transition between two levels in the residual nucleus. Fig. 6 presents an example of gamma-ray and neutron detections (from the Ge detector and one liquid scintillator) for the ²⁸Si(n, n'γ)²⁸Si measurements and shows that the 2⁺ → 0⁺ (g.s.) transition in ²⁸Si is very strongly excited.

<figure><img src="image_27.png" /><figcaption>Fig. 4. PSD on a liquid scintillator EJ301 during the measurements. Two gates on the time pulse are used: a short gate in Y-axis and a long gate in X-axis.</figcaption></figure>

<figure><img src="image_28.png" /><figcaption>Fig. 5. Left: time of flight without PSD for the neutron n' between the target and a sample neutron detector. The narrow peak for the coincidence gamma rays and a broader neutron TOF distribution are marked. For t > 100 ns, only the background is present. Right: same signal with PSD. The gamma peak is not selected and only the neutrons n' with some background are present.</figcaption></figure>

### 3.3. Electronic circuit

Fig. 7 presents the simplified electronics block diagram. Time and pulse-height data are acquired event by event for each detector. A buffered read out scheme is used, to enable the acquisition of more than one event per macropulse. The time to convert and transfer the signal in the ADC to the memory modules is about 10 µs. If an event appears, the $T_0$ from the start of the neutron beam is disabled for the next 10 µs. The data are transferred from the memory to the computer 100 µs after the end of the macropulse. Readout of the memory modules is completed before the arrival of the next macropulse.

<figure><img src="image_29.png" /><figcaption>Fig. 6. Gamma-ray spectrum from the Ge detector for the decay of ²⁸Si from the ²⁸Si(n, n'γ)²⁸Si reaction. The line at 1.78 MeV arises from decays of the first excited state in ²⁸Si.</figcaption></figure>

<figure><img src="image_30.png" /></figure>
<figure><img src="image_31.png" /><figcaption>Fig. 7. Electronics blocks diagram for the neutron and γ-ray detectors.</figcaption></figure>

### 3.4. Samples

In the case of neutron inelastic scattering, different scattering samples of natural elements can be used. Up to now, cylindrical samples of silicon (2 cm in diameter, 5 cm long), carbon (2.5 cm in diameter, 3 cm long), molybdenum (10 cm in diameter, 2 cm long) and iron (different combinations of foils) were used for neutron inelastic scattering from $E_n = 1$ to ~20 MeV. In the case of fission neutron spectra measurements, the target is a fission chamber. The double TOF method is used to determine the energy of both incoming and emitted neutrons. Typically, each measurement requires a few weeks of beam time.

### 3.5. Measurement procedure

As explained previously, two TOFs are used to measure the energy of the incident and outgoing neutrons. In the case of neutron inelastic scattering, the gamma ray emitted by the excited nucleus

is detected by the Ge or $BaF_2$ detectors. The gamma-ray energy indicates that a particular level has been excited. Consequently, it indicates the nature of the residual nucleus when there is more than one possible reaction.

In general neutron-induced reactions, the residual nucleus is in a highly excited state which subsequently decays via a gamma-ray cascade to the ground state or via neutron or light-charged particle emission. Because there is sufficient angular momentum in the system to populate a rather wide range of residual states, few of these states, except the lowest state, decay directly to the ground state and nearly all decay through the first excited state. For inelastic reactions, direct transitions for even-even nuclei to the ground state are unlikely because of the many other possible decay modes. In this case, a coincidence measurement between the gamma decay from the first excited state and the outgoing neutron emission provides information on the levels excited in residual nucleus.
# 4. Data reduction and correction

## 4.1. Neutron detector efficiency

The neutron-detector efficiency was measured using the fission neutrons from a spontaneous fission source of $^{252}$Cf. A total of 38 500 fission events were obtained with TOF between fission-fragment events from the $^{252}$Cf target and pulses from the neutron detectors. The measured signal was the sum of the background and the $^{252}$Cf fission neutron emission. The background, mainly due to scattered neutrons from the experimental area, was extracted from the measured spectrum by a fit for $E_n > 20$ MeV, with the polynomial $B(E) = a_0 + a_1 * E_n + \cdots + a_5 * E_n^5$ where the constants $a_0 \cdots a_5$ are the parameters of the fit. This polynomial is chosen to obtain the best fit of the background at high neutron energy (in the energy range where the neutrons from the fission of $^{252}$Cf have a negligible contribution compared to the background) and to minimize its order. Then this function was used for $E_n < 20$ MeV to separate the background from the $^{252}$Cf neutron spectrum. In Fig. 8 the measured $^{252}$Cf spectrum with the background subtracted is shown. This fission spectrum was then compared to the $^{252}$Cf neutron emission spectrum reference from the Nuclear Energy Agency (NEA) [24] and the efficiency ($^{252}$Cf$_{measured}$/$^{252}$Cf$_{NEA}$) is calculated, see Fig. 8.

<figure><img src="image_32.png" /><figcaption>Fig. 8. Normalization functions: background-free $^{252}$Cf spectrum from FIGARO with the NEA $^{252}$Cf spectrum and the calculated efficiency (in dashed line).</figcaption></figure>

This efficiency is comparable to the calculated detection efficiency for the liquid scintillator NE213 [25]. The ratio of the measured spectrum without background and the NEA $^{252}$Cf spectrum $S(E)/N(E)$ is used to correct the measured spectra for the neutron detector efficiency.

## 4.2. Data reduction

In order to sum the data from all neutron detectors, we present the data as a plot of the excitation energy $E_x$ of the residual nucleus as a function of the incident neutron energy $E_n$. $E_x$ is evaluated by subtracting the ground-state mass from the invariant mass of the residual nucleus of the reaction, for instance $^{28}$Si(n, n')$^{28}$Si. The small momentum of the detected gamma ray is not included in the kinematics. Furthermore, in order to correct the data for the background at all incident neutron energies, several measurements were carried out without the sample, with the neutron beam on. This background, suitably normalized, was subtracted from the sample measurements. By subtraction of the ground-state energy from the total energy, the excitation energy $E_x$ as a function of $E_n$ is then available. Three examples for the neutron inelastic scattering on $^{28}$Si, $^{56}$Fe and $^{12}$C are presented in Figs. 9–11.

In the following, the $^{28}$Si(n, n')$^{28}$Si reaction will be studied in more detail. In order to extract data proportional to cross-section from the $E_x - E_n$ matrix, one-dimensional energy spectra were generated by summing TOF bins corresponding to a “slice” in neutron energy, and projecting onto the excitation energy axis (Y-axis). Then, the excitation energy distribution for a given incident neutron energy is compared with the GNASH and EMPIRE II calculations, as described below.

# 5. Typical results

As a typical result, the neutron inelastic scattering on natural Si from 4 to 20 MeV is presented. In natural silicon, $^{28}$Si has an abundance of 92.2% and thus is a simple target for a first experimental study and for testing model calculations. Additionally, the spectroscopy of excited states of $^{28}$Si
<figure><img src="image_33.png" /><figcaption>Fig. 9. Excitation energy of the residual nucleus <sup>28</sup>Si (MeV) as a function of the incident neutron energy (MeV) after normalization. See specially the excited levels at 1.78, 4.62 MeV with 4.98, 6.28 and 6.69 MeV.</figcaption></figure>

<figure><img src="image_34.png" /><figcaption>Fig. 10. Excitation energy of the residual nucleus <sup>56</sup>Fe (MeV) as a function of the incident neutron energy (MeV) after normalization. See specially the excited levels at 0.85, 2.08 and 2.95 MeV with 2.96 and 3.08 MeV.</figcaption></figure>

has been well studied so that we know that, for the <sup>28</sup>Si(n, n')<sup>28</sup>Si reaction, most of the excited states of <sup>28</sup>Si decay through its first excited state. Only four levels have branches that go directly to the ground state [26]. Thus, for incident neutron energies lower than the effective threshold for the (n,2n) [Q = −17.18 MeV], (n, n'p)[Q = −11.58 MeV] or (n, n'α)[Q = −9.98 MeV] reactions, the measurement of the neutron emission n' of <sup>28</sup>Si(n, n')<sup>28</sup>Si in coincidence with the 1.78 MeV transition from the first 2<sup>+</sup> excited state to the ground state is approximately equal to the measurement of the neutron emission of <sup>28</sup>Si(n, n')<sup>28</sup>Si, see Fig. 12.

<figure><img src="image_35.png" /><figcaption>Fig. 11. Excitation energy of the residual nucleus <sup>12</sup>C (MeV) as a function of the incident neutron energy (MeV) after normalization. See specially the excited level at 4.44 MeV. Note here the background for low beam energies which was not completely eliminated.</figcaption></figure>

### 5.1. Statistical model calculations

Model calculations for neutron reactions on silicon were performed with two different codes, EMPIRE II [27] and GNASH [28,29].

EMPIRE II is a code for nuclear reaction calculations [27]. It includes various nuclear models, designed for calculations in a broad range of energies and incident particles. The version used here (EMPIRE II.16.2) includes the spherical optical model SCAT2 [30], coupled channels (ECIS) [31] and Multistep Direct (ORION + TRISTAN) [32] mechanisms, Monte Carlo pre-equilibrium emission, and the full-featured Hauser-Feshbach model with width fluctuation correction. A comprehensive library of input parameters covers nuclear masses, optical model parameters, ground-state deformations, discrete levels and decay schemes, level densities, moments of inertia, and gamma-ray strength functions. EMPIRE II is used here with the default parameters to calculate the inelastic cross-section <sup>28</sup>Si(n, n')<sup>28</sup>Si and neutron emission spectra. For incident neutron energy less than 10.3 MeV, the reactions <sup>28</sup>Si(n, n'α)<sup>24</sup>Mg and <sup>28</sup>Si(n, n'p)<sup>27</sup>Al are not allowed and the results from EMPIRE II can be directly compared with the measurements on FIGARO. For incident neutron energies higher than the 10.3 MeV threshold, the (n, n'α) channel is open and is in
<figure><img src="image_36.png" /><figcaption>Fig. 12. (n, n'), (n, n'p), (n, n'α), (n, p) and (n, α) channels for the reaction $^{28}$Si + n.</figcaption></figure>

competition with the neutron inelastic scattering channel on $^{28}$Si. The measured cross-sections on FIGARO will then be different from the calculated results, which include all the possible channels (n, n'x). The (n, n'p) channel further complicates the comparison above 12.5 MeV.

The GNASH pre-equilibrium-statistical model code applies Hauser–Feshbach compound nucleus theory to describe the decay of equilibrated nuclei and the exciton model for the emission of higher energy pre-equilibrium ejectiles in the early stage of the reaction [33]. Pre-equilibrium corrections based upon the exciton model of Kalbach [34], modified to include nuclear surface effects, are applied to the decay of the first compound nucleus. The Hauser–Feshbach calculation accounts for sequential multiparticle and gamma-ray decay until secondary emission is complete and the residual nucleus is left in its ground state. Up to six types of radiation can be emitted from each compound system so that in one calculation a maximum of 60 reaction paths can be treated. The GNASH calculations were performed by M. Chadwick and P. Talou from the Theoretical Division (T-16) of the LANL [33].

Neither GNASH or EMPIRE II provides exclusive spectra, therefore the calculated and measured spectra can be compared as long as the (n, n') channel is the only open channel.

## 5.2. Code-measurements comparisons

For both GNASH and EMPIRE II codes, the calculations provide neutron emission intensities with narrow distributions corresponding to the excitation of discrete levels. The output of the codes give widths corresponding to the energy steps taken into account in the calculations. For the measurements, the width of the neutron distribution in the discrete excited-levels region comes from the resolution given by the time of flight between the Si target and the neutron detectors. As the TOF distance for the emitted neutrons is constant (approximately 1 m), the resolution is a function of the outgoing neutron energy $E_{n'}$. The resolution is better for slow neutrons and worse for fast neutrons. In terms of the excitation energy of the residual nucleus, for a given incident neutron energy, this corresponds to a better resolution for a high excitation energy.
In order to compare the measurements with the calculations, a convolution is performed between the gamma-ray peak of the discrete excited level and a Gaussian function with the following parameters:

* centroid equal to the gamma-peak centroid,

* area equal to the gamma-peak area,

* width $\sigma_E$ determined by the TOF energy resolution for the neutron detector to Si target distance. With the hypothesis that the width of the Gaussians is only equal to the TOF resolution, the width is:

$$ \sigma_{E_{n'}} = \Delta E_{n'} \\ = 2E_{n'}\Delta t/t, $$

where $t = \sqrt{ml^2/2E_{n'}}$ is the neutron TOF, $m$ the neutron mass, $l$ the distance from the Si target to the neutron detector ($\approx 1$ m) and $\Delta t$ is the time resolution (1.4 ns) with the $BaF_2$ gamma-ray detector. In these conditions, $\sigma_E$ is then

$$ \sigma_{E_{n'}} = 4 \times 10^{-2} E_{n'}^{3/2}, \qquad (1) $$

where the energies are expressed in MeV. In the continuum region, the excitation of the residual nucleus is high compared to the discrete levels region and the resolution for the outgoing neutron energy is rather good. In consequence, the widths of the Gaussian functions in this energy region are small enough not to enlarge the results from the GNASH and EMPIRE II calculations. Each gamma peak given by EMPIRE II and GNASH is convoluted with a Gaussian with the parameters defined as before. Furthermore, in order to compare the calculations from EMPIRE II and GNASH with the measurements, the intensities corresponding to the population of the four excited levels that do not decay to the first excited level {6.88 MeV (3⁻), 7.38 MeV (2⁺), 7.41 MeV (2⁺) and 7.93 MeV (2⁺)} have to be subtracted from the results of the two codes.

Because the 1.78 MeV gamma ray has an angular distribution not included in the calculations, we need to normalize experiment and calculations. Up to 13 MeV, the FIGARO data are normalized to the mean value given by the integration of EMPIRE II and GNASH data over the excitation energies for a given incident neutron

energy. For higher energies, as the EMPIRE II and GNASH data are the sum of $(n, n')$, $(n, n'\alpha)$ and $(n, n'p)$ reactions, the FIGARO data are not normalized to EMPIRE II and GNASH, but are presented on the same graph and are arbitrarily normalized to compare the shape of each distribution and not the intensities. As explained previously, neutron-emission spectra as a function of the residual excitation energy can be obtained from Fig. 9 for a given incident neutron energy. For excitation energies higher than 8 MeV, the excited levels are no longer discrete and become a continuum region with observable structures. In order to obtain data proportional to the inelastic neutron scattering cross-section as a function of the $^{28}$Si excitation energy for a given incident neutron kinetic energy, narrow slices are projected on the Y-axis in Fig. 9 for incident neutron energies in the range $E_n-E_n+k$. For $E_n$ less than 7 MeV the slice widths $k$ are equal to 200 keV and for higher $E_n$, because of the lower statistics, the slice widths $k$ are equal to 1 MeV. Emission spectra are given in Figs. 13 and 14.

First of all, it is interesting to note that EMPIRE II and GNASH do not give the same intensities for the discrete level distribution or for the continuum region. The input parameters for GNASH have been chosen to give good agreement with previous experimental data on $^{28}$Si(n, xα) and $^{28}$Si(n,xp) [3], whereas for EMPIRE II the input parameters are chosen by default.

In the case where only the $(n, n')$ channel is open, i.e. for incident neutron energies lower than 10 MeV, the measurements show a good agreement with the calculations. Several peaks are well defined at: 1.78, 6.27 and 6.69 MeV. Furthermore, the two neutron peaks at 4.61 and 4.98 MeV are not resolved. For excitation energy higher than 8 MeV, the energy spacings between levels are too small to allow a peak separation and the continuum region begins. The opening of the $(n, n'\alpha)$ and $(n, n'p)$ channels (see Fig. 9) induces a difference between the calculations and the measurements; both calculation codes provide the energy distribution of the first emitted neutron from $^{29}$Si, without a coincidence window on the transition gamma ray between the first excited state and the ground state following the gamma-ray cascade in $^{28}$Si. In consequence, the
<figure><img src="image_37.png" /><figcaption>Fig. 13. Angle-integrated neutron inelastic scattering spectra for neutron energies from 4 to 11 MeV, normalized to the mean area (cross-section) of the calculations. The solid and dashed lines depict the results of EMPIRE II and GNASH calculations when available, performed at the midpoint of the respective neutron energy bin, and convoluted with the resolution of the measurement. The dotted line is the measurement limit.</figcaption></figure>
<figure><img src="image_38.png" /><figcaption>Fig. 14. Angle-integrated neutron inelastic scattering spectra for neutron energies from 12 to 19 MeV, normalized to the mean area (cross-section) of the calculations up to 13 MeV. The solid and dashed lines depict the results of EMPIRE II and GNASH calculations when available, performed at the midpoint of the respective neutron energy bin, and convoluted with the resolution of the measurement. The dotted line is the measurement limit.</figcaption></figure>

codes provide the first-neutron-emission cross-section, which can differ from the inelastic neutron cross-section when the other channels such as $^{28}$Si(n, n'xα) and $^{28}$Si(n, n'xp) are open (for incident neutron energies higher than ~14 MeV).

Furthermore, the emission neutron spectrum is increasing for high excitation energy. This is due to coincidences between the emitted neutrons and gamma rays with energies close to 1.78 MeV which become more important with the opening of the
other decay channels. The present measured data
cannot therefore be normalized to the calculations.

6. Conclusion and perspectives

We have established the new experimental
apparatus FIGARO and methods for the mea-
surement of neutron inelastic scattering in the
MeV region at WNR. By using two TOFs with a
well-collimated white neutron beam, information
of the neutron emission spectra for the reaction
²⁸Si(n, n')²⁸Si in coincidence with the first excited
to the ground-state transition, i.e. 2⁺–0⁺ transition
of the ²⁸Si for incident neutron energies from 4 to
20 MeV are obtained. Comparisons with the
GNASH and EMPIRE II statistical codes show
good agreement as long as no other channels than
(n, n') are opened. The flexibility of FIGARO also
allows measurements of fission-neutron spectra
from neutron-induced fission.

Based on the positive results with the present
FIGARO array of detectors, we plan to increase
the number of neutron detectors to 49 to improve
the efficiency of neutron–gamma coincidence, to
increase the flight path length between the sample
and neutron detectors in order to improve the
resolution and to extend the domain of investiga-
tion up to 100 MeV of incident neutron energy.
With the improved gamma–neutron coincidence
efficiency, we will be able to study nuclear-level
densities over a wide range of nuclei, including
closed-shell, rotational, and fission product nu-
clides. The next improvement for the quality of the
data will depend on a better evaluation of the
neutron detector efficiency at high neutron energy.
For this, we plan to measure the neutron flux with
a EJ 301 scintillator directly in the neutron beam
at low current. Furthermore, in the close future,
the GNASH code will provide exclusive calcula-
tions of (n, n'γ) spectra which will allow an easier
comparison between the calculations and measure-
ments at high neutron energies.

Acknowledgements

We wish to thank M. Chadwick and P. Talou
from the theoretical group in T-16, LANL, for

their collaboration and support for the GNASH
calculations.

References

[1] Intermediate energy nuclear data for applications, Pro-
ceedings of the Advisory Group Meeting, organized by the
International Atomic Energy Agency, Vienna, Oct. 1990,
published by IAEA Nuclear Data Section.

[2] J.F. Ziegler, W.A. Lanford, Science 206 (1979) 776.

[3] F.B. Bateman, R.C. Haight, M.B. Chadwick, S.M. Sterbenz, S.M. Grimes, H. Vonach, Phys. Rev. C60 (1999) 064609.

[4] N.B. Sullivan, J.J. Egan, G.H.R. Kegel, P. Harihar, Nucl. Sci. Eng. 70 (1979) 294.

[5] H.H. Knitter, M. Coppola, Z. Phys. 207 (1967) 56.

[6] D.M. Drake, J.C. Hopkins, C.S. Young, H. Conde, A. Sattler, Nucl. Phys. 128 (1965) 209.

[7] S.C. Mathur, W.E. Tucker, R.W. Benjamin, I.L. Morgan, Nucl. Phys. 73 (1965) 561.

[8] S. Kliczewski, Z. Lewandowski, Nucl. Phys. A304 (1978) 269.

[9] J. Martin, D.T. Stewart, W.M. Currie, Nucl. Phys. A113 (1968) 564.

[10] ENSDF Library, National Nuclear Data Center, BNL,
http://ie.lbl.gov/ensdf.

[11] G.A. Petitt, S.G. Buccino, G.E. Hollandsworth, P.R. Bevington, Nucl. Phys. 79 (1966) 231.

[12] D. Seeliger, D. Schmidt, T. Streil, Nucl. Phys. A460 (1986) 265.

[13] A. Takahashi, E. Ichimura, Y. Sasaki, H. Sugimoto, Double and single differential neutron emission cross-section at 14.1 MeV, Vol. 1, OKTAVIAN Report A-87-03, Osaka University, November 1987.

[14] L. Zanini, A. Aprahamian, Study of reactions of fast neutrons with nuclei with FIGARO at LANSCE, Proceedings of the 15th International Conference on Applications of Accelerators in research and industry, 4–7 November 1998, Denton, TX, USA.

[15] M.B. Chadwick, P.G. Young, S. Chiba, S.C. Frankle, G.M. Hale, G. Hughes, A.J. Koning, R.C. Little, R.E. McFarlane, R.E. Prael, L.S. Waters, Nucl. Sci. Eng. 131 (1999) 293.

[16] D. Rochman, R.C. Haight, J.M. O'Donnell, M. Devlin, Inelastic neutron scattering on Si from 4 to 20 MeV at FIGARO, in: Proceedings of the Sixth International Meeting on Nuclear Applications of Accelerator Technology AccApp'03, June 1–5, 2003, San Diego, CA, in press.

[17] T. Ethvignot, T. Granier, P. Casoli, R.O. Nelson, R.C. Haight, M. Devlin, R. Drosg, N. Fotiadis, J.M. O'Donnell, W. Younes, P.E. Garret, J.A. Becker, Experimental studies of prompt neutron and photon emission in intermediate energy neutron-induced fission, in J.H. Hamilton, A.V. Ramayya, H.K. Carter (Eds.), Proceedings of the Third International Conference on Fission and
Properties of Neutron-Rich Nuclei, Sanibel Island, Florida, November 3–8, 2002, World Scientific, p. 418; LAUR-03-0478.

[18] P.W. Lisowski, C.D. Bowman, G.J. Russel, S.A. Wender, Nucl. Sci. Eng. 106 (1990) 208.

[19] S.A. Wender, S. Balestrini, A. Brown, R.C. Haight, C.M. Laymon, T.M. Lee, P.W. Lisowski, W. McCorkle, R.O. Nelson, W. Parker, Nucl. Instr. and Meth. A 336 (1993) 226.

[20] R.C. Haight, M. Devlin, J.M. O'Donnell, T. Ethvignot, T. Granier, LANL Internal Report, LALP-02-174, 2002.

[21] Eljen Technologie, P. O. Box 870, Sweetwater, TX 79556, URL: http://www.eljentechnology.com/ej-301.htm.

[22] D.T. Ingersoll, B.W. Wehring, Nucl. Instr. and Meth. 147 (1977) 551.

[23] K.H. Maier, J. Nischke, Nucl. Instr. and Meth. 59 (1968) 227.

[24] Nuclear Data Standards for Nuclear Measurements, NEA Nuclear Data Committee, NEANDC/INDC, 1991.

[25] D. Hermsdorf, K. Pasieka, D. Seeliger, Nucl. Instr. and Meth. 107 (1973) 259.

[26] P.M. Endt, Nucl. Phys. A633 (1998) 1.

[27] M. Herman, R. Capote-Noy, P. Obložinský, A. Trkov, V. Zerkin, Recent development and validation of the nuclear reaction code EMPIRE, International Conference on Nuclear Data for Science and Technology, October 2001.

[28] P.G. Young, E.D. Arthur, A preequilibrium, statistical nuclear-model code for calculation of cross-sections and emission spectra, LANL Internal Report LA-6947-C.3, 1977.

[29] E.D. Arthur, The Gnash preequilibrium statistical model code, LANL Internal Report LA-UR-88-382, 1988.

[30] O. Bersillon, SCAT2: Un programme de modèle optique sphérique, Report CEA-N-2227, NEANDC(FR), INDC(E) 49/L, October 1981.

[31] J. Raynal, Notes on ECIS, Report CEA-N-2772, 1994.

[32] T. Tamura, T. Udagawa, H. Lenske, Phys. Rev. C26 (1982) 379.

[33] P.G. Young, E.D. Arthur, M.B. Chadwick, in: A. Gandini, G. Reffo (Eds.), Proceedings of the IAEA Workshop on Nuclear Reaction Data and Nuclear Reactors-Physics, Design, and Safety, 1996, World Scientific Publishing, Singapore, 1998, p. 227.

[34] C. Kalbach, Z. Phys. A283 (1977) 401.
## 2.5 Phys. Lett. B575: Mesure de l'énergie moyenne des neutrons de fission avec FIGARO
<figure><img src="image_39.png" /></figure>

ELSEVIER

# Prompt-fission-neutron average energy for $^{238}$U(n, f) from threshold to 200 MeV

T. Ethvignot$^{a,1}$, M. Devlin$^b$, R. Drosg$^b$, T. Granier$^a$, R.C. Haight$^b$, B. Morillon$^a$, R.O. Nelson$^b$, J.M. O'Donnell$^b$, D. Rochman$^b$

$^a$Commissariat à l'Énergie Atomique, DAM Ile-de-France, BP 12, 91680 Bruyères-le-Châtel, France

$^b$Los Alamos Neutron Science Center, MS H855, Los Alamos National Laboratory, NM 87545, USA

Received 27 June 2003; received in revised form 8 September 2003; accepted 10 September 2003

Editor: V. Metag

## Abstract

Energy distributions of prompt neutrons in coincidence with fission induced on $^{238}$U were measured for incident neutron energies up to 200 MeV. The double time-of-flight technique was used to deduce incident and emitted neutron energies. The experimental average and standard deviations of the fission neutron spectra (FNS), for emitted neutron energies from 0.65 to 7.5 MeV, are reported. The results compare well to predictive calculations with the improved Los Alamos model below 20 MeV incident neutron energy. The observed dip at the opening of the second chance fission channel at 6 MeV is confirmed and analyzed. Above 20 MeV, the experimental results of the FNS are smaller than the calculated ones. At 50 MeV and higher, the data suggest a slight increase of the temperature and the kinetic energy of the fission fragments.
© 2003 Elsevier B.V. All rights reserved.

**Keywords:** Neutron-induced fission; FIGARO; Double time-of-flight technique; Los Alamos model; Watt parametrization

## 1. Introduction

Interest in obtaining a more detailed understanding of prompt neutron emission in fission is now high. To date, there are about half a dozen fission neutron spectra (FNS) compiled in nuclear data libraries for neutron induced fission on $^{238}$U at various energies below and at 14 MeV. No data are available on a

broad, continuous range of incident neutron energies. Such measurements are now possible. The data are of great importance in the connection of accelerator-coupled nuclear reactor systems (ADS) burning and incinerating actinides, with $^{238}$U considered as a prototype actinide. The spallation reactions used to relax the neutron economy of fast nuclear reactors reach to high energy neutrons, which are investigated for the first time in the experiment presented. Moreover, these data would provide valuable information to improve our understanding of fission at high excitation energy. In particular, it is interesting to investigate in which proportions the heated system releases the excess of

<footnote>E-mail address: thierry.ethvignot@cea.fr (T. Ethvignot).

¹ Partially supported by Délégation Générale pour l'Armement of the French Ministry of Defense.</footnote>
energy with pre-fission neutron and charged particle emission and increase of excitation energy and angular momentum of the primary fragments. As a matter of fact, a theoretical effort has been pursued recently [1,2], to predict the properties of prompt neutron emission in fission at high excitation energies. Prompt fission neutrons are characterized by two basic quantities, the average number of prompt neutrons emitted per fission, which is known up to 30 MeV [3], and the neutron energy spectrum which is not nearly as well known. However, it was shown for a few cases that not only the average energy but also the shape of the FNS depends on the incident neutron energy [4–6]. The fission neutrons are emitted from various sources. At low energies, the main source of neutrons is their evaporation from fission fragments (FFs) from first chance fission. With increasing energy the mixture of fissioning systems with different masses complicates the overall pattern. Also, the emission of pre-equilibrium neutrons prior to fission can contribute to a high-energy tail of the FNS [7,8]. In our measurement we do not distinguish between neutrons emitted before and after fission.

In order to analyze and discuss the data in the next sections, we used the Los Alamos model to calculate the FNS for comparison with data. The starting point of the model is the Weisskopf theory for neutron evaporation from a fragment at a given excitation energy calculated using the triangular prescription by Terrell [9] as a function of nuclear temperature. The neutron energies in the center of mass are transposed to the laboratory frame by assuming isotropic emission from average heavy and light fragments. As the incident neutron energy goes up, higher-chance fission channels open. The laboratory spectra are then weighted by the recently evaluated partial fission cross sections [10]. Pre-fission neutrons, statistically emitted from the compound nucleus, are also accounted for in the FNS. A primary advantage of the Los Alamos model is its predictive power [11].

A simplified approach, but one which represents both experiment and models, is to fit the FNS with a Watt parameterization [12]. In the center of mass, a Maxwellian distribution is assumed for the energy of the neutrons emitted from the decaying fragments with a temperature $T_e$ and an average kinetic energy per nucleon $E_f$. Then in the laboratory frame, the FNS is simply described by a two parameter func-

tion

$$N_w(E) \cdot \frac{2A^{3/2}}{(\pi B)^{1/2}} \exp \cdot \frac{B}{4A} \exp(\cdot AE) \cdot \sinh(BE)^{1/2}, \quad (1)$$

where the Watt parameters are related to the physical quantities by the relations $A \cdot 1/T_e$ and $B \cdot 4E_f/T_e^2$. The average neutron energy of the Watt distribution is simply given by

$$E \cdot \frac{3}{2} T_e \cdot E_f. \quad (2)$$

The parametrization has a limited accuracy, but it is a useful approximation to describe FNS with low statistics. Also, the average neutron energy is derived analytically, and therefore is not sensitive to details of the spectral shape near the chosen upper and lower thresholds.

## 2. Experiment and data selection

The experiment was performed on the FIGARO beam line [13] installed at the WNR spallation source of fast neutrons [14] at the Los Alamos National Laboratory. The neutrons are created by an 800 MeV proton beam on an unmoderated tungsten target, with an average proton current of 5 µA. The beam structure consisted of short micro-pulses 1.8 µs apart, grouped in a 625 µs beam gate at a repetition rate of 100 Hz. The incident neutron spectrum was similar to a Maxwellian distribution with a temperature of about 2 MeV and a high energy tail. The FIGARO setup was situated at 22 m from the neutron source and 30 deg with respect to the incident proton beam. The beam was collimated to a spot size of 1.3 cm diameter at the sample position. The double time-of-flight (TOF) method was used. The incident neutron energy was derived from the time difference between the proton pulse in the production target and the fission pulse in a fission chamber. The energy of fission neutrons was derived from the time difference between the fission chamber pulse and a neutron detector pulse.

The 94-layer ionization fission chamber, containing • 380 mg of pure $^{238}$U, was • 10 cm long. Each layer consisted of a stainless steel backing with deposits of
2 mg of $^{238}$U on both sides. The fission rate was typ-
ically 300 s⁻¹. But, because of the 6.25% duty fac-
tor of the proton beam, the instantaneous fission rate
rose higher than 10 000 s⁻¹. Discrimination between
fission fragments, α particles and noise was excel-
lent, and no bias to the detected fragment distribution
was assumed. The time resolution of 7 ns (FWHM) of
the chamber was deduced from the photo-fission peak
induced by the γ-ray flash accompanying the proton
pulse. The time-resolution associated error on the in-
cident neutron energy ranged from 17 keV at 1.6 MeV
to 29 MeV at 200 MeV.

Neutron detectors were used for the experiment.
They consisted of scintillation-liquid-filled cells that
are 12.5 cm in diameter and 5 cm thick coupled to
photo-multiplier tubes. Three detectors were put at
112 cm from the fission chamber at laboratory angles
90, 105 and 120 deg, and two at 218 cm and angles
around 90 deg on the opposite side. The detection
angles were chosen to minimize the sensitivity of the
results to pre-equilibrium neutrons, which are emitted
preferentially in the forward direction.

A classical pulse-shape discrimination, based on
short-time and long-time scintillation light compo-
nents, was applied to the data off-line to eliminate
γ-ray events. This discrimination sets a lower limit
for the detection of neutrons to several hundreds of
keV. However, the residual background in the emitted
neutron TOF spectrum had to be reduced by applying
an additional requirement on selected events. Indeed,
a group of events exhibited a large light deposition
but a low emitted neutron energy calculated from the
TOF. These unusable events were attributed to acci-
dental coincidences of fission and scattered neutrons.
This selection set the FNS threshold to 0.65 MeV for
our experiment. The spectra recorded with the detec-
tors at 218 cm could not be used because of the re-
maining background level. The time resolution of the
neutron detectors was much less than that of the fission
chamber, i.e., 2 to 3 ns (FWHM). An overall time reso-
lution of 7.5 ns (FWHM) was deduced from the fission
prompt γ-ray peak in the raw TOF spectrum. The as-
sociated error on the detected neutron energy ranged
from 15% at 0.65 MeV (low threshold) to 50% at
7.5 MeV (high threshold). A total of 650 000 neutron-
fission coincidences were recorded during 14 days of
actual beam time and for incident neutron energies up
to 200 MeV.

A set of 59 FNS spectra was extracted from
the TOF spectra. The statistics were summed over
the detectors. In the analysis process, the digital
value of the TOF of an event was replaced with
a real number chosen at random between the two
consecutive digits defining the bin. The weight of
the event was taken from a normalized trapezoidal
interpolation with a slope determined from the local
derivative of the distribution. Then, the energy was
calculated analytically from the TOF real value and the
distribution was stored in a 50 keV per bin spectrum. It
was checked that the procedure did not bias the values
of the average and standard deviation of the FNS.

The incident neutron energy bin definitions were
chosen to get similar statistics in each bin. With about
11 000 counts in each bin the statistical error of the
FNS average is less than • 1.5%.

**3. Data analysis and results**

The efficiency of the neutron detectors was de-
termined from the analysis of the energy spectrum
around 2.9 MeV incident neutron energy, where good
reference data are available. The distribution was di-
vided by the precision measurement by Boykov et al.
[15] and fitted to a 6th order polynomial. The shape
of the relative efficiency obtained with this procedure
resembles the typical intrinsic efficiency expected for
a proton recoil scintillator [16], i.e., a sharp threshold
at 0.65 MeV, a maximum at 1.9 MeV and a roughly
constant value above 3.2 MeV. The experimental spec-
trum without and with the normalized efficiency cor-
rection is plotted in Fig. 1. The reference spectrum,
normalized to the raw data spectrum, is also plotted
on the same figure. The efficiency corrected spectrum
matches well the reference spectrum within the statis-
tical uncertainties. However, it underestimates slightly
the reference below 0.8 MeV and overestimates it from
0.85 to 1.1 MeV. This systematic mismatch is due to
the choice of the efficiency function. Since the FNS
statistics are rather low, this simple function was pre-
ferred over a more sophisticated one. Therefore, the
confidence gained over the determination of the effi-
ciency in the range 0.65–7.5 MeV was at the price of
a slight overestimate of the average FNS energy.

All spectra were then corrected for efficiency us-
ing the above prescription. The raw spectrum statis-
<figure><img src="image_40.png" /><figcaption>Fig. 1. Fission neutron spectrum for the system $^{238}$U(n, f) measured with the FIGARO setup. Data are for incident neutron energies from 2.1 to 4.0 MeV and are compared to a precision measurement at 2.9 MeV incident neutron energy [15].</figcaption></figure>

tical error was propagated in each bin. The average neutron energy and standard deviations were simply computed from the statistical analysis of the distribution, applying upper and lower thresholds. The experimental values and the values calculated from the Los Alamos model are plotted in Fig. 2 for comparison. The shape of the distribution up to 20 MeV is very similar to that given by the Los Alamos model. The main features of the FNS average are a dip at 6 MeV, corresponding to the opening of the second chance fission, and a mismatch above 20 MeV, as the calculated values strongly overestimate the data.

In order to reduce the sensitivity of the FNS average to the choice of the efficiency function and the values of the thresholds, the Watt parametrization was used. Both experimental and calculated (Los

Alamos model) FNS were fitted with the function of Eq. (1). Then, Eq. (2) was simply used to calculate the FNS average. The error bars were calculated from the propagation of the errors of the fitted parameters A and B, typically 5 and 20% for the experimental spectra. The experimental and calculated values are plotted in Fig. 3. The absolute values confirm the trends discussed for Fig. 2, but the error bars are three times larger, because statistical and systematic uncertainties are added. The dominant term, i.e., the partial error with respect to A, sets the precision of the FNS average to • 5%.

It is also worth noting that the confidence level of the fit of the FNS with a Watt function was comparable at all incident neutron energies. This means that, for this study of the FNS average, low and high
<figure><img src="image_41.png" /><figcaption>Fig. 2. Neutron spectrum average energy (upper plot) and standard deviation (lower plot) for neutrons emitted from neutron-induced fission of $^{238}$U where only emission energies in the range 0.65 to 7.5 MeV are considered. The data are compared with the Los Alamos model [1,2] with the same restriction on emitted energies.</figcaption></figure>

incident neutron energy spectra can be approximated by Watt functions with the same precision, i.e., the impact of the higher energy portion of the spectrum is statistically negligible.

4. Discussion and conclusion

The average value provides less detailed information than precise measurements of FNS, but it was measured and calculated with good precision over a wide range of incident neutron energy for $^{238}$U(n, f). The results are not sensitive to pre-equilibrium neutrons and high-energy neutrons because of the fitting procedure and because the angles at which neutron

detectors were placed biased against pre-equilibrium neutrons. The agreement within errors with the well-tested Los Alamos model calculations up to 20 MeV incident neutron energy validates the experimental procedure. Looking in closer detail at the calculations, one can interpret the dip at 6 MeV as the observation of a transition from first to second chance fission, resulting in a net effect of a 10% decrease of the average energy. Indeed, the relative fission cross-section for the first chance drops from 100% to 30% between 5 and 7 MeV, whereas it rises from 0% to 70% for the second chance in the same range according to a recent evaluation [10]. Above 20 MeV, the calculation overestimates the data. It is also interesting to analyze the gross trend of the FNS av-
<figure><img src="image_42.png" /><figcaption>Fig. 3. Fission neutron spectrum average for the system $^{238}$U(n, f) as a function of the incident neutron energy. Experimental and calculated spectra were fitted with a two parameter Watt function (see Eq. (1)). The average energy is analytically calculated from Eq. (2). Points represent the experimental data and a curve is given for the calculated spectra.</figcaption></figure>

erage energy from 2 MeV (just above threshold) to 2.5 MeV (at 200 MeV incident neutron energy). Temperature and kinetic energy per nucleon of the fission fragments were obtained from the fitted parameters of the experimental and calculated FNS with Eq. (1). For this purpose, it was necessary to re-bin the experimental data by 3. The results, plotted in Fig. 4, show that these quantities slightly increase above 50 MeV. The finding that the FNS changes so little is surprising considering the range of incident energies of mostly 2 orders of magnitude. This might be an indication that only a small proportion of the additional excitation energy of the fissioning system is released through heating processes of the primary fragments.

In conclusion, it was shown that experimental tools have recently become available to investigate fission neutron spectra for a broad range of incident neutron energies. The first results with a $^{238}$U target are reported in this Letter. The results were interpreted with the Los Alamos model which is well constrained and validated at low incident neutron energies. The observed sharp transition from first to second chance fission results in a 10% decrease in the average energy. Finally, a slight increase of the fission fragment temperature and kinetic energy from threshold to 200 MeV is deduced from the analysis. The results presented in this Letter are the starting point of a more comprehensive future program. In order to measure the missing portions of the FNS, where previous
<figure><img src="image_43.png" /><figcaption>Fig. 4. Temperature (upper plot) and kinetic energy per nucleon (lower plot) of the fission fragments for the system $^{238}$U(n, f) as a function of the incident neutron energy. The values were obtained from the fit of the experimental and calculated (Los Alamos model) FNS with a Watt function. The Watt parameters are represented with points for the experimental data and as a curve for the calculations.</figcaption></figure>

experiments have shown significant deviations from a pure Maxwellian distribution, many more detectors will be mounted. They will be positioned farther off to measure neutron energies above 7.5 MeV, shielded to reduce the reported experimental threshold of 0.65 MeV, and set at various angles to investigate the emission of pre-equilibrium neutrons. Also, these experiments will be carried out with other targets of importance, e.g., $^{235}$U, $^{239}$Pu, $^{237}$Np, which are readily available.

## Acknowledgements

We thank Dr. D.G. Madland for his enthusiastic support of the experimental program. Portions of this

work and the LANSCE facility were funded by the US DOE under Contract No. W-7405-ENG-36.

## References

[1] D.G. Madland, J.R. Nix, Nucl. Sci. Eng. 81 (1982) 213;
D.G. Madland, Acta Phys. Hungariae New Ser. Heavy Ion
Phys. 10 (1999) 231.

[2] G. Vladuca, A. Tudora, Ann. Nucl. Energy 28 (2001) 1643.

[3] J. Frehaut, et al., IAEA-INDC (NDS)-220 (1988) 99.

[4] A.M. Trufanov, G.N. Lovchikova, M.I. Svirin, A.V. Polyakov, V.A. Vinogradov, V.D. Dmitriev, G.S. Boikov, Phys. At. Nucl. 64 (2001) 1.

[5] P. Staples, J.J. Egan, G.H.R. Kegel, A. Mittler, M.L. Woodring, Nucl. Phys. A 591 (1995) 41.

[6] F.-J. Hambsch, S. Oberstedt, G. Vladuca, A. Tudora, Nucl. Phys. A 709 (2002) 85.
[7] T. Kawano, T. Ohsawa, M. Baba, T. Nakagawa, Phys. Rev. C 63 (2001) 034601.

[8] T. Miura, et al., in: K. Shibata (Ed.), Proc. Int. Conf. Nuclear Data for Science and Technology (ND2001), Tsukuba, Japan, 7–12 October, 2001, J. Nucl. Sci. Technol. Suppl. 1 (2) (2002) 409.

[9] J. Terrell, Phys. Rev. 113 (1959) 527.

[10] M. López-Jiménez, P. Romain, Evaluation of partial fission cross-sections of $^{238}$U and $^{239}$Pu, private communication, 2003.

[11] D.G. Madland, in: A.R. Bishop (Ed.), Special Feature 2001, Supplement of the T-Division Self-Assessment for 2000, Los Alamos National Laboratory LA-UR-01-1847 (2001) 112.

[12] C. Wagemans, The Nuclear Fission Process, CRC Press, 1991.

[13] R.C. Haight, J.M. O'Donnell, L. Zanini, M. Devlin, D. Rochman, in: Proceedings of the Eleventh International Symposium on Capture Gamma-Ray Spectroscopy and Related Topics, Pruhonice, Czech Republic, September 2–6, 2002, in press.

[14] P.W. Lisowski, C.D. Bowman, G.J. Russell, S.A. Wender, Nucl. Sci. Eng. 106 (1990) 208.

[15] G.S. Boykov, V.D. Dmitriev, G.A. Kudyaev, Yu.B. Ostapenko, M.I. Svirin, G.N. Smirenkin, Yad. Fiz. 53 (1993) 628.

[16] G. Knoll, Radiation Detection and Measurement, 2nd Edition, Wiley, New York, 1989.
2.6 Phys. Rev. Lett. 94: Mesure de la multipli-cité moyenne des neutrons de fission avec FI-GARO
Neutron Multiplicity in the Fission of <sup>238</sup>U and <sup>235</sup>U with Neutrons up to 200 MeV

T. Ethvignot,<sup>1,*</sup> M. Devlin,<sup>2</sup> H. Duarte,<sup>1</sup> T. Granier,<sup>1</sup> R. C. Haight,<sup>2</sup> B. Morillon,<sup>1</sup> R. O. Nelson,<sup>2</sup> J. M. O'Donnell,<sup>2</sup> and D. Rochman<sup>2</sup>

<sup>1</sup>Commissariat à l'Énergie Atomique, DAM Ile-de-France, DPTA/Service de Physique Nucléaire, BP 12, 91680 Bruyères-le-Châtel, France

<sup>2</sup>Los Alamos Neutron Science Center, Los Alamos National Laboratory, MS H855, Los Alamos, New Mexico 87545, USA
(Received 7 July 2004; published 11 February 2005)

Prompt-fission-neutron multiplicities were measured for <sup>238</sup>U(n, f) and <sup>235</sup>U(n, f) from 0.4 to 200 MeV. The data are of great importance in connection with accelerator-coupled nuclear reactor systems incinerating actinides. We report that fission induced by 200 MeV neutrons produces ≈10 more prompt neutrons than fission induced by reactor neutrons. Most neutrons are evaporated from the fission fragments and the prefission compound nucleus, as the preequilibrium emission of energetic neutrons accounts for a maximum of 15% of the prompt neutrons at 200 MeV.

DOI: 10.1103/PhysRevLett.94.052701

PACS numbers: 25.85.Ec, 24.75.+i, 28.41.–i

Efforts are being pursued in measuring [1,2] and modeling [3–7] prompt-fission-neutron properties from low to intermediate energies. The knowledge of neutron multiplicities and the characteristics of fission neutrons are of particular interest in connection with the development and design of accelerator-driven systems (ADS) for the transmutation of nuclear wastes [8]. Moreover, these data provide valuable information on the fundamental understanding of the neutron-induced fission process. In particular, it is interesting to investigate in which proportions the heated system releases the excess energy with pre-fission neutron and light charged particle (LCP) emission on the one hand, and increase of excitation energy and angular momentum of the primary fragments on the other hand. Prompt-fission-neutron multiplicities (the average of which is denoted by $\bar{v}_p$) for neutron-induced fission of uranium were measured by Fréhaut [9] in the 1970s from 1.5 to 28 MeV for <sup>235</sup>U and <sup>238</sup>U. Howe et al. [10] completed the measurement up to 49 MeV for <sup>235</sup>U(n, f) in the 1980s. But beside points on <sup>238</sup>U(n, f) at energies below 60 MeV [11], only one measurement was reported at intermediate energies at 156 MeV [12]. The availability of an intense “white” neutron source combined with an efficient fission vs neutron coincidence setup made it possible to investigate prompt-fission neutron spectra for the first time for <sup>238</sup>U(n, f) over a wide range of energies [1]. The results reported in this Letter for both <sup>238</sup>U(n, f) and <sup>235</sup>U(n, f) for $\bar{v}_p$ bear important information on the emission process that imply consequences for the design of industrial applications of nuclear fission at intermediate energies.

Two methods are commonly used to measure prompt-fission neutron multiplicities. The first one consists of detecting the neutrons emitted in the reaction with a large, nearly $4\pi$, Gd-loaded liquid scintillator ball. The method is appropriate for absolute measurements of the first and second moments of the multiplicity distribution with good precision since most neutrons, low to high energy, are detected [9]. However, it is not well suited for

measurements over a wide incident neutron energy range as it requires long irradiation times with monoenergetic beams. Also, no information on the energy of the detected neutrons is obtained. The second method utilized in this work consists of detecting the neutrons with smaller liquid scintillators at a distance from a target sensitive to fission fragments. A double time-of-flight technique is used to determine the incident neutron energy and the emitted neutron energy to build the fission neutron spectrum (FNS) as a function of the incident neutron energy [10]. A quantity proportional to $\bar{v}_p$ is simply obtained from the ratio of the integration of the FNS to the number of fission events. The measured quantities depend on the detection angles and energy thresholds, and therefore they have larger systematic errors than the Gd detector data. However, the technique is well suited to measurements with a white neutron source and permits the investigation of angular distributions. The measurements reported here were carried out on the FIGARO beam line [13] at the Weapons Neutron Research (WNR) spallation source of fast neutrons and the details of the analysis are discussed in [1]. The experiment with uranium 238 (235) was performed with a proton micropulse spacing of 1.8 μs (4.3 μs). A fission chamber containing 382 mg (348 mg) of pure uranium 238 (235) was situated at 22 m from the neutron source and used as the target for fission events. Three neutron detectors were used for the analysis. The liquid scintillator cells were cylinders of 12.5 cm in diameter and 5 cm in thickness. The center faces were positioned at 1.143, 1.143, and 1.143 m (0.905, 0.905, and 0.875 m) from the target and at angles 105°, 90°, and 120° (116°, 71°, and 85°).

The efficiency of the neutron detectors was determined relative to a reference spectrum, i.e., a neutron spectrum of evaporation from fission fragments calculated with the Los Alamos model (see the next section) for neutron-induced fission at 1.5 MeV incident neutron energy ($E_n$). This reference spectrum is well matched to a large body of experimental data. The ratio of our experimental spectrum
around 1.5 MeV to the reference spectrum was fitted to a sixth order polynomial. The ratio was normalized at the maximum of the spectrum, i.e., between 1 and 2 MeV detected neutron energy. The useful range of the emitted neutron spectra was from 0.8 to 7.5 MeV. Outside of this range the efficiency was set to zero. The relative average neutron multiplicities were simply computed from the integration of the FNS distributions divided by the number of fissions in the incident neutron energy bins. Our data are normalized (using least square minimization) to reference data [9] between 1.5 and 28 MeV incident neutron energy. The experimental values for $^{238}$U(n, f) [ $^{235}$U(n, f)], as well as the data of [9], are plotted in Fig. 1 [Fig. 2]. The vertical error bars represent the systematic errors from the normalization; the horizontal ones represent the experimental resolution of the energies of the incident neutrons. Existing sparse data points [10,12] at intermediate energies are also presented for comparison. The neutron detectors in the case of Cheifetz et al. [12] were at 90° to the beam. There was also a coincidence required between the fission fragment (one detector at 90° to the beam and the other in the forward direction). The plan was to detect neutrons at 90° or 0° relative to the direction of emission of the fission fragments. In other words, there were similarities and differences with our work. Similar to our work, the neutrons were not detected in the forward direction. Different from our work, a coincidence was required with fission fragments at two chosen angles in order to evaluate the proportion of neutrons emitted from the moving fragments to prefission neutrons. In our work, kinematic effects are averaged over. One should also note that the fissility of the p + $^{238}$U system is greater than that of n + $^{238}$U and so the two may not be directly comparable. The present $\bar{\nu}_p$

<figure><img src="image_44.png" /><figcaption>FIG. 1. Prompt-fission neutron average multiplicity for the system $^{238}$U(n, f) as a function of incident neutron energy (open circles). Our data are not corrected for the undetected neutrons but are normalized to the data from [9] (black dots). One $^{238}$U(p, f) experimental point is plotted (×) [12].</figcaption></figure>

data follow a simple exponential function: $\bar{\nu}_p(E_n) = p1 + [p2 - p1][1.0 - \exp(-p3 \times E_n)]$, where p1 represents the value of $\bar{\nu}_p$ at very low energy, and p2 represents the extrapolation of the maximum number of emitted neutrons at very high energies. This function was used by Wahl to parametrize fission yield systematics up to 200 MeV [14]. The data were fitted with this simple function. The fit parameter values are given in the plots. One can see that the difference between neutrons emitted in the fission of uranium 238 and 235 increases from 4% at low energies to 9% at 200 MeV. At this energy, one more neutron is emitted on average for uranium 238. In order to analyze the source of the emitted neutrons, and the potential bias of the experimental energy and angular cuts, we have made calculations that are discussed in the next section.

Two models with low- and high-energy descriptions were used to interpret the reported data. At low energies, it was assumed that the number of neutrons detected at side angles and forward angles was the same. Indeed, though anisotropy of fragment emission relative to the beam can be large [15], the effect on neutron anisotropy was found to be negligible. For energies up to 30 MeV for uranium 235 and 50 MeV for uranium 238, the prompt-fission neutron multiplicities and spectra were analytically calculated using the Los Alamos (LA) model [7] modified by Vladuca and Tudora [16]. In this model, the prompt-fission neutron multiplicity is obtained from an energetic balance ratio. The available energy (the average fission energy released minus the average fission-fragment kinetic energy minus the average prompt gamma ray energy) is divided by the average energy carried away by the neutron (the average fission-fragment neutron separation energy plus the average center-of-mass energy of the emitted neutrons). The

<figure><img src="image_45.png" /><figcaption>FIG. 2. Prompt-fission neutron average multiplicity for the system $^{235}$U(n, f) as a function of incident neutron energy (open circles). Our data are not corrected for the undetected neutrons but are normalized to the data from [9] (black dots). Data from [10] are plotted with a +.</figcaption></figure>
main feature is the dependence of the average total fission-fragment kinetic energy and the average gamma energy on neutron incident energy. The fission cross section probabilities were calculated with the statistical model up to the fifth chance for uranium 235 and the eighth chance for uranium 238 [17].

At intermediate energies, neutron emission in fission is not isotropic and preequilibrium emission cannot be neglected. Therefore, it was necessary to simulate the experiment with a Monte Carlo model that includes the three neutron emission mechanisms. Indeed, inelastic reactions induced by nucleons may be described by an intranuclear cascade (INC) model followed by evaporation and fission models. The INC describes the interactions of energetic particles with nucleons of the target nucleus as individual collisions [18]. The particles produced are emitted in the continuum in less than $10^{-20}$ s, and the remaining nucleus is often highly excited [19]. The deexcitation of the residual nucleus is achieved by slower sequential emission of neutrons and LCPs, but not yet $\gamma$ rays, competing with fission. Only events leading to fission, the vast majority for the higher incident neutron energies, are included. The codes that treat each process use the Monte Carlo technique. Therefore, it is straightforward to simulate the experimental cuts on energy and emission angle of the produced particles. The Bruyères-le-Chatel INC code named BRIC [19] was developed for the simulation of ADS systems for a wide range of elements and incident energies. The performance was optimized for a single element, lead, a typical ADS target. The code is based on an approximation of the relativistic 3D simulation of the Boltzmann equation where nucleons are Dirac functions in phase space. The evaporation code is based on the statistical emission theory of Weisskopf-Ewing [20]. The emission probabilities are determined with the energy-dependent level density function from a backshifted Fermi-gas model [21]. The cross sections of the inverse process of emission are based on existing data. The fission process is simulated with the Rutherford Appleton Laboratory model of Atchison [22]: this model gives the probability for fission at each step of the deexcitation stage, i.e., the ratio of fission to neutron emission widths. But in our case, the emission widths of LCPs are also considered. Therefore, the fission probability was adjusted to reproduce reasonable fission cross sections for a wide range of incident energies. The fission-fragment distributions were chosen at random within the prescribed parametrization. In the last step of the calculation, the fission fragments release the residual excitation energy after scission through evaporation of neutrons and LCPs.

The comparison of the data to the model calculations is plotted in Figs. 3 and 4. The average energy $\langle E \rangle$ of the FNS is shown in the upper part. It was obtained from a fit to the experimental FNS with a Watt function in order to get the average over all neutron energies and thus an average that is not sensitive to the experimental thresholds [1]. The error bars were calculated from the propagation of the

<figure><img src="image_46.png" /><figcaption>FIG. 3. Prompt-fission neutron average energy (upper plot) and multiplicity (lower plot) for the system $^{238}$U(n, f) as a function of incident neutron energy measured with the FIGARO setup.</figcaption></figure>

errors of the fitted Watt parameters. For $^{238}$U, the error bars are smaller than in the data reported previously [1] because of the use of larger incident energy bins and different threshold definitions. Experimental values (open circles) are compared to the LA model calculations at low energies (thin line). The average neutron multiplicity $\bar{\nu}_p$ is plotted in the lower part of the figures. Experimental values (open circles) are compared to the LA model calculations at low energies (thin line) and the BRIC calculations (thick lines) above 20 MeV. With the BRIC calculations, energy

<figure><img src="image_47.png" /><figcaption>FIG. 4. Prompt-fission neutron average energy (upper plot) and multiplicity (lower plot) for the system $^{235}$U(n, f) as a function of incident neutron energy measured with the FIGARO setup.</figcaption></figure>
and angular cuts were applied to match the experiment conditions. We also represent the BRIC calculated total emission into $4\pi$ values (no energy or angular cuts) to illustrate the discussion (thick dashed line). The values of $\bar{v}_p$ with energy and angular cuts were normalized to the first calculated point at 20 MeV of $\bar{v}_p$ without cuts to facilitate the comparison of the experimental and calculated values. The shapes of $\langle E \rangle$ and $\bar{v}_p$ are well reproduced with the LA model, but there are differences above 20 MeV. The dip observed for $\langle E \rangle$ around 6.5 MeV is confirmed with the uranium 235 target, although it is not as deep as for uranium 238. The reason for this might be that the first chance fission probability for uranium 235 is larger than that for uranium 238. And so the contribution from second chance fission is relatively larger for uranium 238; i.e., there is a bigger change at the second chance fission threshold for uranium 238. The calculated values for $\bar{v}_p$ at higher energies exhibit some differences with the data, but the agreement is better than 10% over the whole experimental range. The Monte Carlo calculations also indicate that in the fission of uranium 235 (238) at 200 MeV the source of the neutrons can be attributed to fast intranuclear cascade emission for 15% (15%), to pre-fission evaporation for 10% (15%) and to evaporation from the fission fragments for 75% (70%) of the total. From the comparison of the calculations of $\bar{v}_p$ with and without energy and angular cuts we deduce that the measurement is underestimated by 10%, at most, for the highest incident neutron energy, and that those undetected neutrons are mostly high-energy, forward-peaked INC neutrons.

In conclusion, new data on $\bar{v}_p$ and $\langle E \rangle$ are reported with errors $\le 15\%$. $\bar{v}_p$ grows steadily in the fission of $^{238,235}$U induced by neutrons up to 200 MeV. At this energy, it exceeds by $\approx 10$ the number of neutrons from fission induced by reactor neutrons. Uranium 238 shows enhanced neutron emission compared to uranium 235 due to the higher mass and lower binding energy of the neutrons. Beyond the scientific understanding of the fission process, these results are important for the assessment and control of future ADS reactor neutronics and reactivity, affecting projections of the criticality, efficiency, safety, and lifetime of such systems. In future experiments, we plan to investigate on a much broader range the energy and the angular distributions of the emitted neutrons to improve the precision of the data.

We thank Dr. D. G. Madland for his enthusiastic support of the experimental program, and Dr. V. M. Maslov for fruitful discussions. T. E. was partially supported by Délégation Générale pour l'Armement of the French Ministry of Defense.

O'Donnell, and D. Rochman, Phys. Lett. B 575, 221 (2003).

[2] V. N. Dushin, F.-J. Hambsch, V. A. Jakovlev, V. A. Kalinin, I. S. Kraev, A. B. Laptev, D. V. Nikolaev, B. F. Petrov, G. A. Petrov, V. I. Petrova, Y. S. Pleva, O. A. Shcherbakov, V. I. Shpakov, V. E. Sokolov, A. S. Vorobyev, and T. A. Zavarukhina, Nucl. Instrum. Methods Phys. Res., Sect. A 516, 539 (2004).

[3] F.-J. Hambsch, S. Oberstedt, A. Tudora, G. Vladuca, and I. Ruskov, Nucl. Phys. A726, 248 (2003).

[4] V. M. Maslov, Yu. V. Porodzinskij, M. Baba, A. Hasegawa, N. V. Kornilov, A. B. Kagalenko, and N. A. Tetereva, Phys. Rev. C 69, 034607 (2004).

[5] A. Tudora, G. Vladuca, and B. Morillon, Nucl. Phys. A740, 33 (2004).

[6] T. Kawano, T. Ohsawa, M. Baba, and T. Nakagawa, Phys. Rev. C 63, 034601 (2001).

[7] D. G. Madland and J. R. Nix, Nucl. Sci. Eng. 81, 213 (1982); D. G. Madland, Acta Phys. Hung. New Ser.: Heavy Ion Phys. 10, 231 (1999).

[8] D. Kerdraon, A. Billebaud, R. Brissot, B. Carluec, S. David, D. Heuer, C. Le Brun, E. Liatard, J.-M. Loiseaux, and O. Meplan, Prog. Nucl. Energy 42, 11 (2003).

[9] J. Fréhaut (private communication).

[10] R. E. Howe, Nucl. Sci. Eng. 86, 157 (1984).

[11] V. A. Rubchenya, W. H. Trzaska, D. N. Vakhtin, J. Aysto, P. Dendooven, S. Hankonen, A. Jokinen, Z. Radivojevic, J. C. Wang, I. D. Alkhazov, A. V. Evsenin, S. V. Khlebnikov, A. V. Kuznetsov, V. G. Lyapin, O. I. Osetrov, G. P. Tiourin, A. A. Aleksandrov, and Yu. E. Penionzhkevich, Nucl. Instrum. Methods Phys. Res., Sect. A 463, 653 (2001).

[12] E. Cheifetz, Z. Fraenkel, J. Galin, M. Lefort, J. Peter, and X. Tarrago, Phys. Rev. C 2, 256 (1970).

[13] D. Rochman, R. C. Haight, J. M. O'Donnell, M. Devlin, T. Ethvignot, and T. Granier, Nucl. Instrum. Methods Phys. Res., Sect. A 523, 102 (2004).

[14] A. C. Wahl, Los Alamos Report No. LA-13928, 2002.

[15] R. Vandenbosch and J. R. Huizenga, *Nuclear Fission* (Academic Press, New York, London, 1973), p. 196, Fig. VI-14.

[16] G. Vladuca and A. Tudora, Annals of Nuclear Energy 28, 689 (2001).

[17] M. López-Jiménez and P. Romain (private communication).

[18] H. Bertini, Phys. Rev. 188, 1711 (1969); J. D. Stevenson, Phys. Rev. Lett. 41, 1702 (1978); Y. Yariv and Z. Fraenkel, Phys. Rev. C 20, 2227 (1979); V. S. Barashenkov et al., Nucl. Phys. A338, 413 (1980); J. Cugnon, Nucl. Phys. A462, 751 (1987).

[19] H. Duarte, in *Proceedings of the 10th International Conference on Nuclear Reaction Mechanisms, Varenna, 2003*, edited by E. Gadioli (Università Degli Studi Di Milano, Milano, 2003), pp. 607-616.

[20] V. F. Weisskopf and D. H. Ewing, Phys. Rev. 57, 472 (1940).

[21] A. V. Ignatyuk, G. N. Smirenkin, and A. S. Tishin, Sov. J. Nucl. Phys. 21, 255 (1975).

[22] F. Atchison, in *Proceedings of a Specialists' Meeting, OECD/NEA, Issy-les-Moulineaux, France, 1994* (OECD, Issy-les-Moulineaux, 1994).

<footnote>*Electronic address: Thierry.Ethvignot@cea.fr</footnote>

<footnote>[1] T. Ethvignot, M. Devlin, R. Drosg, T. Granier, R. C. Haight, B. Morillon, R. O. Nelson, J. M.</footnote>
2.7 Phys. Rev. Lett. 101: Réponse à un commentaire de Kornilov et Hambsch
**Ethvignot et al. Reply:** The physical conclusions developed in the preceding Comment [1] are largely in agreement with our Letter [2]. Nevertheless, it is asserted that our results on the mean energy and multiplicity of the fission neutrons are in disagreement with each other. Our evaluation procedure is blamed and considered to be the source of the discrepancy. We do not agree with these two assertions and will explain why in this Reply.

Neutrons emitted coincidently with fission can be divided into: (1) neutrons emitted by the deexciting fragments and (2) neutrons emitted before scission (prefission). Emission from the fragments is isotropic in the center of mass frame and is characterized by a Maxwellian or better, a Watt energy spectrum. As for prefission emission, at low incident neutron energy, it follows the laws of the compound nucleus and is thus also isotropic and characterized by a Maxwellian spectrum. At higher incident energy, say above 14 MeV, the emission of neutrons before equilibrium (or preequilibrium) can occur. It exhibits a forward-peaked angular distribution and an energy distribution extending up to about the energy of the incident particle. As stated in Ref. [2] and in our previous article [3], in the experiments reported, the detectors were placed at angles around 90° and measurements were performed in the 0.8–7.5 MeV domain of emitted neutron energy. Thus, most of the preequilibrium neutrons were missed. This is confirmed by the measured shapes of the neutron spectra which are compatible with Watt functions for all incident energies [3]. A discussion on the number of preequilibrium neutrons missed is included in Ref. [2] on the basis of calculations with the BRIC code which describes preequilibrium and fission-evaporation [4]. For $\bar{\nu}$, an agreement within 10% in the energy range (20–200 MeV) between data and BRIC calculations including the experimental cuts in angle and energy is observed (Figs. 3–4 in Ref. [2]). Also, it is found that the application of these cuts results in a loss in $\bar{\nu}$ of ~10% at 200 MeV, rapidly decreasing at lower incident energy: ~1.5% at 50 MeV. The discussion in Ref. [2] concludes that the preequilibrium neutrons unaccounted for in the measurements amounts to ~10% at 200 MeV. No comment is made on the impact on the mean neutron energy. This may be seen as a shortcoming that might cause confusion. However, we insist on the agreement and consistency of the experimental results presented in Ref. [2] (Figs. 3–4), namely, the mean neutron energy and the mean multiplicity as measured by our experiments. These results correspond to the same experimental data. They do not account for preequilibrium neutrons and never were intended to as stated in the text and shown in the figure labels “Watt Average Energy.” We include here in Fig. 1 the results for the mean neutron energy from the BRIC calculations for $^{235}$U. The dashed line corresponds to the mean energy of all neutrons. The full line represents the mean energy obtained after applying the experimental acceptance cuts (angles and energy) by a fit with a Watt

<figure><img src="image_48.png" /><figcaption>FIG. 1. Mean fission neutron energy for $^{235}$U(n, f) as a function of incident neutron energy. The experimental data points are those of Ref. [2]. The BRIC calculations are for all neutrons and for neutrons measured in the experiment of Ref. [2]. See text for details.</figcaption></figure>

function. It can be seen that at 200 MeV, the fraction of the mean neutron energy corresponding to the missed preequilibrium neutrons is ~75% although the same calculation shows that only ~10% of the number of neutrons is missed [2]. The good agreement with the experimental points of Ref. [2] should be noted. We stress that no parameters of the model were adjusted to our data whatsoever.

We are grateful to the authors of the Comment for the opportunity to clarify our results. We agree on the fact that preequilibrium neutrons emitted coincidently with fission were not measured and on the consequences for the mean neutron energy. This is in total agreement with our Letter. Our results are confirmed by relevant model calculations (see also Ref. [5]). They provide new constraints on nuclear reaction models and are thus valuable for applications such as accelerator-driven systems.

T. Ethvignot,¹ M. Devlin,² H. Duarte,¹ T. Granier,¹

R. C. Haight,² B. Morillon,¹ R. O. Nelson,²

J. M. O'Donnell,² and D. Rochman²,*

¹CEA-DAM

Bruyères-le Châtel, 91297 Arpajon Cedex, France

²Los Alamos National Laboratory

MS H855, Los Alamos, New Mexico 87545, USA

Received 24 January 2008; published 18 July 2008

DOI: 10.1103/PhysRevLett.101.039202

PACS numbers: 25.85.Ec, 24.75.+i, 28.41.−i

*Now at NRG, Westerduinweg 3, P.O. Box 25, NL-1755 ZG, Petten, The Netherlands

[1] N. V. Kornilov and F.-J. Hambsch, preceding Comment, Phys. Rev. Lett. **101**, 039201 (2008).

[2] T. Ethvignot et al., Phys. Rev. Lett. **94**, 052701 (2005).

[3] T. Ethvignot et al., Phys. Lett. B **575**, 221 (2003).

[4] H. Duarte, Phys. Rev. C **75**, 024611 (2007).

[5] V. A. Rubchenya, Phys. Rev. C **75**, 054601 (2007).
# Chapitre 3

## Annexe : Détection de particules α et résolution spatiale des cellules solaires

La mise en oeuvre des cellules solaires avec le préamplificateur de charge SAPHIR (Cf. 2.1) présente de nombreux avantages: compacité, temps de monté rapide, temps de relaxation relativement rapide, insensibilité aux rayonnements ionisants (hors fragments de fission et fortes doses). Cependant, pour certaines applications futures, on a voulu établir la compacité des cellules solaires à la détection des particules α. C'est ce qui est montré sur la figure 2. On compare la réponse en énergie d'une cellule solaire irradiée par une source de 252Cf semi-épaisse (les α et les fragments traversent les feuilles qui la contiennent, mais avec une perte d'énergie de 30 à 50 %) avec le préamplificateur SAPHIR et un préamplificateur de spectroscopie commercial. La distribution des fragments de fission est comparable, mais on constate que le préamplificateur CAMBERRA permet de parfaitement détecter les particules α avec 100% d'efficacité. Avec le préamplificateur SAPHIR, les α et le bruit ne sont pas discriminés.

Ensuite, avec le même montage de la cellule et du préamplificateur CAMBERRA, on a mesuré la résolution en énergie pour les particules α. Le résultat est porté sur la figure 3. On y compare la réponse à une source α trois corps de la cellule et d'une jonction Si de spectroscopie. La résolution de la cellule aux α est, comme pour les fragments de fission, de l'ordre de 20%.
<figure><img src="image_49.png" /></figure>

<footnote n="2">²Comparaison de la réponse en énergie d'une cellule solaire à l'irradiation par une source de 252Cf avec deux préamplificateurs.</footnote>
<figure><img src="image_50.png" /></figure>

<figure><img src="image_51.png" /></figure>

<footnote n="3">³Comparaison de la résolution en énergie d'une cellule solaire et d'une jonction Si de spectroscopie à l'irradiation par une source α trois corps.</footnote>
D'autre part, on a étudié la résolution spatiale des cellules solaires. Pour ce faire, on a découpé une lamelle de 56×8mm dans une cellule plus grosse. A chaque extrémité était connecté un préamplificateur SAPHIR. Un masque était placé sur la cellule. La source de 252Cf irradiait la cellule à travers une fente de 2 mm placée à différentes positions (x). On a ainsi observé les impulsions dues aux fragments de fission en fonction de leur éloignement à une extrémité. Lorsque la source est proche d'une extrémité, l'impulsion est très rapide (5ns) et haute. La même impulsion à l'autre extrémité est retardé. Son temps de monté est beaucoup plus long (50 ns), et sa hauteur plus basse. En effet, la charge collectée est la même à chaque extrémité.

Différentes voies ont été explorées pour obtenir la meilleure résolution en position à partir de l'exploitation de la forme des impulsions. C'est la différence en temps, ou TAC, qui donne le meilleur résultat. Chaque sortie du préamplificateur est mise en forme par un amplificateur de temps rapide (intégration=différenciation = 20ns), suivi d'un discriminateur à fraction constante (retard externe = 10ns). Sur la figure 4 on montre les TAC obtenus en plaçant la source à chaque extrémité. L'écart entre les deux gaussiennes donne le temps relatif (T) de transit d'une impulsion d'une extrémité à l'autre (x=54mm). La largeur relative ($\frac{\Delta T}{T}$) permet de déduire la résolution en position:

$$ \Delta x = x \frac{\Delta T}{T} $$

En l'occurence, on obtient une résolution de $\Delta x = 8$mm. On compare les résultats avec une cellule nue (noir) et une cellule posée sur une feuille de cuivre de même dimensions. Les signaux sont plus rapides avec la feuille de cuivre, mais la résolution spatiale reste identique.

La résolution spatiale de 8mm obtenue, quoique médiocre en comparaison des performances de détecteurs de position commerciaux, permet d'envisager la conception d'un détecteur d'axe de fission compact, $4\pi$, de forme cylindrique à base polygonale: chaque lamelle de cellule constituant un des pans du cylindre.
<figure><img src="image_52.png" /></figure>

<figure><img src="image_53.png" /></figure>

<footnote n="4">⁴Résolution en position d'une cellule solaire déduite de la différence de temps d'arrivée des impulsions aux extrémités.</footnote>