We have performed in-beam γ-ray spectroscopy via fusion-evaporation reaction of a radio-active(RI) beam to investigate high-spin states in (49-51)Ti.

In neutron-rich Ti isotopes, studies of shell structure are gaining recently much attention from both the experimental and theoretical point of view. The appearance of N = 32 and/or 34 sub-shell closures is one of examples of changing the location of single particle orbits in the neutron-rich region. The spectroscopic study at the high-spin yrast states has an advantage to see shell gaps and to test predictions from shell-model calculations, since a single particle states can be arisen in the yrast high-spin states near the closed shell nuclei. In the yrast levels of (50)Ti, large gap in the excitation energy of the levels between 7+ and 6+ states is corresponded to N = 28 shell gap between νf7/2 and νp3/2 neutron orbits according to the shell-model calculations. This shell gaps are also predicted neighbor nuclei of (50)Ti. We have investigated the yrast high-spin states by in-beam γ-ray spectroscopy in (49-51)Ti.

By means of in-beam γ-ray spectroscopy, the fusion-evaporation reaction is commonly used to populate the high-spin states, since a large amount of angular momentum can be brought into the system. However, nuclei produced by the fusion-evaporation reactions using stable isotope beams are limited, in many cases, to the proton-rich side relative to the β-stability line. A usage of a neutron-rich RI beam allows investigation of the high-spin states in the neutron-rich nuclei. We have developed new method to produce a low-energy RI beam for fusion-evaporation reaction, which called as secondary fusion reaction.

Experiment was performed in RIKEN Projectile-fragment spectrometer (RIPS) beam line in RIKEN. The secondary (46)Ar beam was produced by the projectile-fragmentation reaction of a (48)Ca primary beam on a 9Be target. An aluminum curved degrader installed at momentum focal plane was used to achieve a clear isotope separation and to lower the energy of the beam. Almost pure secondary beam was obtained at second focus (F2) of RIPS. The (46)Ar was further lowered in energy using a rotatable aluminum degrader at F2. The intense low-energy RI beam was obtained with An intense low-energy beam with the energy of about 4 MeV/nucleon and with the intensity of 1×10(8) particle per second was successfully obtained. The low-energy beam transported to final focus (F3), where the secondary target of 9(9)Be was placed to induce the secondary fusion reaction, 9Be((46)Ar,xn)(55-x)Ti.

Gamma rays emitted from evaporation residues were detected by an array of germanium detectors: Gamma-Ray detector Array with Position and Energy sensitivity (GRAPE) together with two clover and one coaxial detectors placed around the secondary target to cover the angular range between 30° and 130° . The GRAPE provides the position information of the interaction point of detected γ rays by adopted the pulse shape analysis to improve the energy resolution of Doppler-broadened γ rays. The energy resolution after the Doppler correction and the full energy peak efficiency were typically 15 keV and 3.5% for 1.5-keV γ rays.

Data was written in event-by-event bases to disks with trigger condition of two or more germanium detectors firing in coincidence with the beam. A total amount of 1×10(8) events were collected.

Events associated with the fusion evaporation were identified based on the velocity difference between the beam and the fusion products. By gating relatively low-velocity region in the energy spectrum of the outgoing particles, accidental coincidence background mainly from β-decay of the (46)Ar was reduced. Evaporation channel was further separated using a cross-section dependence of the incident beam energy. The energy of (46)Ar beam was distributed between 2 and 8 MeV/u at the center of the target due to the energy straggling after passing through the degraders and the beam-line detectors. By gating on different region of the beam energy spectrum, excitation functions of the each γ rays were obtained for indentification of the evaporation channel for each event.

The data analyses were performed by the novel analysis of excitation function analysis, γ-γ coincidence analysis, and multiplicity measurements. High-spin levels up to (21/2)-, (11+), and (17/2)- were confirmed for (49-51)Ti, respectively. In left side of Fig. 1, proposed level schemes of (49-51)Ti were shown. The high-spin levels at 7050 keV in (49)Ti and at 4406 and 5246 keV in (51)Ti are newly identified in the present investigation, respectively.

The shell-model code ANOTINE was used to calculate the energies and wavefunctions of levels in (49-51)Ti within full pf-shell model space. The calculation were carried out with four Hamiltonians; FPD6, KB3G, GXPF1 and GXPF1A. Almost all features of the calculated yrast levels are similar with these four Hamiltonians. The results from the shell-model calculation are compared with the experimental level schemes in the right hand side in Fig. 1.

A low-lying levels in (50)Ti start with Jπ= 0+,2+,4+,6+ sequence and are due to the dominance of the proten π(f(7/2))2 multiplet according to the calculation. With a simple interpretation, dominant shell components for low-lying states of (49)Ti and (51)Ti are regarded as members of the π(f(7/2))2 (f(7/2))7 and π(f(7/2))2ν(f(7/2))8(p3/2)1 multiplet, respectively.

At the high-spin states, Jπ=8+,9+,10+,11+ sequence in (50)Ti is understood as an one-particle one-hole (1p1h) excitation of the neutron across the N=28 shell gap, ν(f(7/2))(-1)(p(3/2))1, coupled with the two protons with Jp = 6+ in the f(7/2) orbit. The newly observed level at 7050 keV in (49)Ti, which corresponds to 7076-keV state in the shell-model calculation with GXPF1A, is also considered as the neutron 1p1h configuration, π(f(7/2))2ν(f(7/2))6(p(3/2))1. In (51)Ti, two high-spin states in (51)Ti were observed at 4406 and 5246 keV in the present investigation. The (15/2(-)) state at 4406 keV, which corresponds to 4876 keV (15/2(-)) state in the shell-model calculation, is dominated by π(f(7/2))2ν(f(7/2))7(p(3/2))2 configuration. Based on the systematic consideration, this level is also dominated by 1p1h configuration of ν(f(7/2))7(p(3/2))1 as shown of 5865-keV state in the calculation.

In conclusion, we have performed in-beam γ-ray spectroscopy of the high-spin states in (49-51)Ti via the secondary fusion reaction, 9Be((46)Ar,xn) (55-x)Ti. The high-spin levels at 7050 keV in (49)Ti and at 4406 and 5246 keV in (51)Ti are newly identified, respectively. By comparing the full-pf-shell calculation, persistency of N = 28 shell gap is confirmed in these three nuclei.

本論文は6章と一つの付録からなる。第1章は本研究の動機・背景、短寿命核によるインビーム核分光法の特徴がまとめられている。第2章で実験装置、実験条件が説明され、第3章では装置の校正とデータの解析法が解説されている。結果は第4章でまとめられており、第5章で議論と考察を行い、第6章で本研究をまとめている。

第1章では最近の研究から中性子過剰核領域の中性子魔法数28近傍において殻構造の変化が見いだされつつある事を示し、粒子軌道f7/2-(p3/2,P1/2,f5/2)間に存在するギャップエネルギーの系統的研究の重要性を指摘した。さらにインビーム核分光実験によるイラスト準位の観測が殻構造研究の重要な手段となる事を示し、新たに短寿命核ビームによる(49-51)Ti原子核のインビーム核分光実験を提案した。

第2章では実験装置、実験条件が説明されている。実験は理化学研究所の入射核破砕片分離装置(RIPS)から得られる40MeVIAの(46)Arビームを用いて行われた。(9)Be標的との核融合反応による残留核、(49-51)Tiを生成するには4MeV/A程度のビームエネルギーが必要となる。物質を通過させてエネルギーを下げる場合、不純物の混入や空間的広がりの増大でビーム強度の低下が引き起こされる。申請者は(46)Arの生成標的厚さ、RIPS中間焦点面のエネルギー損失板の厚さを独自の手法で最適化し、純度100%の(46)Arビーム生成に成功した。最終的には9Be標的直上流のエネルギー損失板で微調整を行い、2~6MeV/Aの(46)Arビームを得ている。

検出器系は、ビームの位置・エネルギー情報を得るためのビーム検出器群と、残留核から放出される脱励起ガンマ線検出用の18台の位置感応型Ge検出器(GRAPE)、2台の4分割Ge検出器(CLOVER)と1台の同軸型Ge検出器からなる。

第3章では検出器の校正と得られたデータの解析手法の説明がされている。残留核は、ビーム検出器で測定された(46)Afビームと残留核のエネルギー差を使って特定される。検出されたガンマ線エネルギースペクトル上のドップラー補正はGRAPEの出力波形解析により行われる。複雑な波形解析に対する申請者の地道な努力によって初めて、エネルギー分解能の高いスペクトルが得られ、統計的に小さなガンマ線ピークの発見が可能となった。なお波形解析の詳細は付録に詳述されている。ガンマ線を放出した残留核の同定および励起準位の構築には、個々のガンマ線の角度分布、多重度、ビームエネルギーに対するガンマ線の強度分布や他のガンマ線との同時計数情報が用いられた。

第4章において(49-51)Tiの高励起状態の準位構築が行われている。本研究では、これまでに報告された(49-51)Tiのガンマ線を確認するとともに、(49)T1由来の2664keVのガンマ線と、このガンマ線を放出する7046KeVの励起状態の発見、(51)Ti由来の761,837,2495keVのガンマ線を発見した。また(49)Tiの7046keV状態のスピン・パリティ、(51)Tiの5246,4406,3646keV状態の準位構造とスピン・パリティを示唆することができた。

第5章では励起準位を殻模型計算と比較し、(49)Ti,7046keV,Jπ=(21/2)-状態、(50)Ti,6125keV,Jπ=7+状態、(51)Ti,5246keV,Jπ=(17/2)-状態が、f(7/2),p(3/2)中性子軌道間の1plh配位として記述できる事を示した。これらの準位の下に位置するイラスト準位との大きなエネルギー差は魔法数28のf(7/2)-p(3/2)間のギャップエネルギーに対応する。さらに(53-55)Feの準位構造との比較から、陽子側のf(7/2)軌道が2粒子状態であるTiと2空孔状態であるFeでは中性子のp(3/2),p(1/2),f(5/2)軌道間のエネルギー差が異なっている可能性を指摘した。

本研究では短寿命核ビームによる初めてのインビーム核分光実験から、中性子過剰核領域における中性子魔法数28の殻構造を調べる事に成功した。この研究で確立された短寿命核によるインビーム核分光法は不安定核領域における核構造研究を切り拓く強力な手法となるであろう。

本論文は19名の研究者との共同研究の成果であるが、実験装置、実験条件の最適化から、実験の遂行、データ解析および考察にわたって申請者が中心となり進めてきたと判断できる。特にGRAPE検出器の徹底した波形解析によりS/N比の良いガンマ線スペクトルを導き、(49-51)Tiの高励起状態の発見とN=28のエネルギーギャップの観測を可能とした点は、研究者としての能力の高さを示すものである。よって審査員全員が本論文を博士(理学)の学位請求論文として合格であると判定した。