Intrinsic Quadrupole Moment Research Articles

Theoretical comparison of transition rate B(E2) and deformation parameter with experimental data for calcium (20Ca) isotopes using shell model theory

A theoretical comparison has been made for some calcium isotopes ([Formula: see text]Ca) which are even–even nuclei and have the atomic mass (Z = 20) with its previous experimental data. Theoretical calculations of some [Formula: see text]Ca isotopes (A = 42, 44, 46, 48, 50, 52) adopted by the shell model theory were performed to calculate the transition rate B(E2), theoretical intrinsic quadruple moments ([Formula: see text] and theoretical deformation parameters ([Formula: see text], [Formula: see text] were calculated by two methods by using different effective interactions for each isotope such as, su3fp, fpbm, fprkb, fpd6, kb3. Through code NuShellX@MSU, the single-body density matrix was calculated. The effects of the core polarization were neglected by adopting various effective charges that were employed, effective charges of conventional (Con-E), effective charges of standard (St-E) and effective charges of Bohr and Mottelson (B-M-E) which were calculated. The theoretical values of the B(E2)Th, the [Formula: see text] and the ([Formula: see text], [Formula: see text] were then compared with the previous experimental data where values of the transition rate B(E2)Th, theoretical intrinsic quadrupole moments [Formula: see text] and theoretical deformation parameter ([Formula: see text], [Formula: see text], using the fpbm, the fpd6 and the kb3 interactions were the best.

Comparison between the theoretical and experimental values of transition rate B(E2), deformation parameters and intrinsic quadrupole moments for some Ti isotopes

In this study, electric quadrupole transition properties in some even-even Ti nuclei have been investigated by using different effective charges and interactions. In this respect, B(E2) transition rates, deformation parameters and intrinsic quadrupole moments have been calculated. In calculations, NuShellX code has been used to calculated one body matrix elements (OBDM). Theoretical calculations on these quantities have been compared with the experimental results, and it has been seen that theoretical values obtained by using the kb3 and vpnp interactions and Bohr Mottelson (B-M) and Standard (S-T) effective charges are close to the corresponding experimental results.

A comparison between theoretical results and experimental data of transition probability B(E2), deformation parameter, and intrinsic quadrupole moments for different nuclei with mass number A = 44

A comparison has been made between theoretical results and the experimental data for different nuclei (even-even) that possess the same mass number A = 44 and which have close values of the experimental deformation parameter such as 16S44, 18Ar44, 20Ca44 and 22Ti44. The core-polarization effects and model space were adopted through the inclusion of effective charges. Transition probability B(E2), theoretical deformation parameters, and theoretical intrinsic quadruple moments were calculated using two different interactions for each case, the first case the hasp interaction for nuclei in the sd shell, and the fpd6 interaction for nuclei in the fp shell, the second case the vpnp interaction for nuclei in the sd shell, and the kb3 interaction for nuclei in the fp shell, as well as adopted to different effective charges, such as Bohr and Mottelson effective charges, standard effective charges, and the effective charges from program NuShellX. The theoretical results of the transition probability B(E2), deformations parameters, and intrinsic quadruple moments were compared and found to be close to the experimental values for these nuclei.

Electric reduced transition probabilities of \(^{186}\text{W}\) and \(^{186}\text{Os}\) isobars through the interacting boson model-I

In this study, we applied the Interacting Boson Model (IBM-I) to compute the electric reduced transition probabilities B(E2)\(\downarrow\) of even-even neutron rich \(^{186}\text{W}\) and \(^{186}\text{Os}\) isobars. The ratio \(R_{4/2} = E(4_{1}^{+}) / E(2_{1}^{+})\) has also been calculated for those isobars and the SU(3) symmetry for those isobars has been reported. \(E(4_{1}^{+})\) and \(E(2_{1}^{+})\) indicate the energy level of \(4_{1}^{+}\) and \(2_{1}^{+}\), respectively. We have described the strength of B(E2) in W.u. for \(^{186}\text{W}\) and \(^{186}\text{Os}\) isobars of some of the low-lying quadrupole collective states in contrast to obtainable measured data. The electric reduced transition probabilities B(E2)\(\downarrow\) from yrast state gamma transition from \(12_1^{+} \rightarrow 10_1^{+}\), \(10_1^{+} \rightarrow 8_1^{+}\), \(8_1^{+} \rightarrow 6_1^{+}\), \(6_1^{+} \rightarrow 4_1^{+}\), \(4_1^{+} \rightarrow 2_1^{+}\) and \(2_1^{+} \rightarrow 0_1^{+}\) and other bands states and B(E2) ratio of \(^{186}\text{W}\) and \(^{186}\text{Os}\) isobars have been compared with obtainable measured data and other previous studies. Also calculated were the systematic strength of B(E2), intrinsic quadrupole moments, and deformation parameters of even-even \(^{186}\text{W}\) and \(^{186}\text{Os}\) isobars. The data from these calculations are in good matching with the obtainable measured data. The IBM-I model for the strength of B(E2) has been systematically deduced in SU(3) limit for a few yrasts states transitions in \(^{186}\text{W}\) and \(^{186}\text{Os}\) isobars.

Systematic Projected Shell Model Study of Even-Even Dysprosium Isotopes

Back-bending phenomenon is one of the important phenomena usually seen at high spin states of even - even heavy nuclei. As a result, any changes in the behavior of nuclear rotation, such as increase in moment of inertia versus rotational frequency can be shown in the usual back-bending plots which have been studied in many papers before. In this paper we show for the first time that these changes can be seen in the ratio of electromagnetic reduced transition probabilities B (E2) and B (M1) in even - even 152-164 Dy isotopes using the Projected Shell Model (PSM) theory. The electric quadrupole transition probability B (E2) and the magnetic dipole transition probability B (M1) moments are sensitive to nuclear shape deformation and nuclear charge distribution, respectively. Our findings confirm the well-known back-bending previously seen and are in good agreement with experimental results. While intrinsic quadrupole moments are constant for each Dy isotope, the new findings show that spectroscopic quadrupole moments are increasing with spin. 15.00 Normal 0 false false false EN-US X-NONE AR-SA /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman","serif";}

Study of Nuclear Radius and Back bending phenomenon of 20-30Mg Isotopes in sdpn Model Space

In present work, many parameters have been computed using NuShellX@ MSU code for ground state bands of 20-30Mg isotopes. These parameters were root mean square of nuclear radius, major and minor of ellipsoid axises (a and b), as well as to the different between them(ΔR) deformation parameters (β2, δ), intrinsic quadrupole moment(Q0) and back bending phenomenon. Model space(sdpn) of (0d3/2,0d5/2 and 1s1/2) for protons and neutrons orbits and cwhcdpn interaction have been used to calculate above parameters. Effective charge of Bohr - Mottelson model has been used in this work. The results showed an brilliant agree with the obtainable investigational results all isotopes in this study. Also, the back bending phenomenon was well evident in our results for all isotopes used under study. In these calculations, new values have been theoretically designated for most parameters which were previously unknown in experimental information.

Smith–Purcell radiation of a vortex electron

A wide variety of emission processes by electron wave packets with an orbital angular momentum ℓℏ, called the vortex electrons, can be influenced by a nonparaxial contribution due to their intrinsic electric quadrupole moment. We study Smith–Purcell radiation from a conducting grating generated by a vortex electron, described as a generalized Laguerre–Gaussian packet, which has an intrinsic magnetic dipole moment and an electric quadrupole moment. By using a multipole expansion of the electromagnetic field of such an electron, we employ a generalized surface-current method, applicable for a wide range of parameters. The radiated energy contains contributions from the charge, from the magnetic moment, and from the electric quadrupole moment, as well as from their interference. The quadrupole contribution grows as the packet spreads while propagating, and it is enhanced for large ℓ. In contrast to the linear growth of the radiation intensity from the charge with a number of strips N, the quadrupole contribution reveals an N 3 dependence, which puts a limit on the maximal grating length for which the radiation losses stay small. We study spectral-angular distributions of the Smith–Purcell radiation both analytically and numerically and demonstrate that the electron’s vorticity can give rise to detectable effects for non-relativistic and moderately relativistic electrons. On a practical side, preparing the incoming electron’s state in a form of a non-Gaussian packet with a quadrupole moment—such as the vortex electron, an Airy beam, a Schrödinger cat state, and so on—one can achieve quantum enhancement of the radiation power compared to the classical linear regime. Such an enhancement would be a hallmark of a previously unexplored quantum regime of radiation, in which non-Gaussianity of the packet influences the radiation properties much stronger than the quantum recoil.

Calculation of quadrupole deformation parameter β2 from reduced transition probability B(E2) for 0+1 → 2+1 transitions at even-even 62-68Zn isotopes

In this work the excited energy levels, reduced transition probabilities B(E2)↑, intrinsic quadrupole moments, and deformation parameters have been calculated for 62-68Zn isotopes with neutrons number N = 32, 34, 36 and 38. NuSheIIX code has been applied for all energy states of fp-shell nuclei. Shell-model calculations for the zinc isotopes have been carried out with active particles distributed in the lp3/2, 0f5/2, and lp1/2 orbits outside doubly magic closed 56Ni core nucleus. By using f5p model space and f5pvh interaction, the theoretical results have been obtained and compared with the available experimental results. The excited energies values, electric transition probability B(E2), intrinsic quadrupole moment Q0, and deformation parameters β2 have appeared in complete agreement with the experimental values. As well as, the energy levels have been confirmed and determined for the angular momentum and parity of experimental values that have not been well established and determined experimentally. On the other hand, it has been predicted some of the new energy levels and electric transition probabilities for the 62-68Zn isotopes under this study which were previously unknown in experimental information.

G factor of the $$12^+$$ K-isomer in $$^{174}$$W

The g factor of the $$12^+$$ K-isomer in $$^{174}$$ W has been measured by means of the time-differential perturbed angular distribution technique as $$g(12^+)=+0.304(11)$$ . In addition, the half-life of the isomer has been remeasured as $$T_{1/2}(12^+)=124(8)$$ ns, in agreement with the literature value and confirming the anomalous hindrance F of the E2 transition to the $$10^+$$ level of the ground state band with respect to the $$\gamma $$ -tunnelling model prediction. The measured g factor has been compared with estimates based on experimental g factors from odd-mass isotopes in the same mass region and with Nilsson model calculations. The results establish unique features of the $$12^+$$ K-isomer in $$^{174}$$ W, which can possess a non-pure intrinsic configuration and/or can be characterised by values of the intrinsic quadrupole moment $$Q_0$$ and the rotational g factor $$g_R$$ significantly different with respect to the majority of K-isomers at mass $$A \approx 180$$ .

Intrinsic electric quadrupole moment of the Kπ=8− isomeric state in Hf178

The lifetime of the ${9}^{\ensuremath{-}}$ state in the rotational band based on the 4.0 s, ${K}^{\ensuremath{\pi}}={8}^{\ensuremath{-}}$, isomeric state ($^{178}\mathrm{Hf}^{{m}_{1}}$) from the decay of the 31-yr isomer ($^{178}\mathrm{Hf}^{{m}_{2}}$) was determined to be 99(2) ps by means of the fast-timing technique using two ${\mathrm{LaBr}}_{3}$(Ce) scintillators. The $\ensuremath{\delta}(E2/M1)$ mixing ratios of the $\mathrm{\ensuremath{\Delta}}I=1\phantom{\rule{4pt}{0ex}}\ensuremath{\gamma}$ rays depopulating levels in this band were deduced from $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ angular correlations by using a $^{178}\mathrm{Hf}^{{m}_{2}}$ radioactive source located at the center of the Gammasphere HPGe detector array. The new results, together with previous spectroscopic information, provide a different way to extract the intrinsic quadrupole moment of ${Q}_{0}=6.45(14)\phantom{\rule{4pt}{0ex}}e\text{b}$ for the $^{178}\mathrm{Hf}^{{m}_{1}}$ band. A possible explanation for the reduction of the $^{178}\mathrm{Hf}^{{m}_{1}}$ nuclear charge radius is presented.

Axisymmetric deformations of neutron stars and gravitational-wave astronomy

Einstein's theory of general relativity predicts that the only stationary configuration of an isolated black hole is the Kerr spacetime, which has a unique multipolar structure and a spherical shape when non-spinning. This is in striking contrast to the case of other self-gravitating objects, which instead can in principle have arbitrary deformations even in the static case. Here we develop a general perturbative framework to construct stationary stars with small axisymmetric deformations, and study explicitly compact stars with an intrinsic quadrupole moment. The latter can be sustained, for instance, by crust stresses or strong magnetic fields. While our framework is general, we focus on quadrupolar deformations of neutron stars induced by an anisotropic crust, which continuously connect to spherical neutron stars in the isotropic limit. Deformed neutron stars might provide a more accurate description for stellar remnants formed in supernovae and in binary mergers, and can be used to improve constraints on the neutron-star equation of state through gravitational-wave detections and through the observation of low-mass X-ray binaries. We argue that, if the (dimensionless) intrinsic quadrupole moment is of a few percent or higher, the effect of the deformation is stronger than that of tidal interactions in coalescing neutron-star binaries, and might also significantly affect the electromagnetic signal from accreting neutron stars.

Study of Deformation Parameters (β2, δ) For 18,20,22,24,26,28Ne isotopes in sdpf shell

The quadrupole deformation is basic to study the shape transitions; it is possible to predict many important properties of even-even nuclei as a function of the deformation parameter. The deformations of nuclei are important for understanding their shapes prolate or oblate. The quadrupole deformation parameters were calculated by the transition probability B (E2) for 18, 20, 22, 24, 26,28Ne isotopes, were adopted different interactions three. The calculations are performed with the Bohr-Mottelson (B-M) effective charges, which represent the effect of the core-polarizations. Also, the deformation parameters were calculated for different nuclei and adopted two methods of calculation: from reduced the transition probability (B2) and from the intrinsic quadrupole moment. In calculations, the Shell model is adopted.

Study of nuclear charge radius

Based on the existing experimental data of nuclear radius, the previous formula of nuclear charge radius is verified and discussed. Comparing the formula of the single-parameter nuclear charge radius, it is proved that the formula of <inline-formula><tex-math id="M4">\begin{document}$Z^{1/3}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20191643_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20191643_M4.png"/></alternatives></inline-formula> law is better than the formula of <inline-formula><tex-math id="M5">\begin{document}$A^{1/3}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20191643_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20191643_M5.png"/></alternatives></inline-formula> law. We refitted the two-parameter formula and the three-parameter formula that have been proposed and confirmed that the two-parameter and three-parameter formula fit better than the single-parameter formula. It is shown that show that the deformation plays a key role in the nuclear charge radius. The electric quadrupole moment is an important physical quantity representing the properties of the nucleus. Its appearance indicates the deviation from spherical symmetry and also reflects the size of the nuclear deformation. The electric quadrupole moment is also one of the basic observations to understand the distribution of matter within the nucleus, to examine the nuclear model, and to observe nucleon-nuclear interactions. Taking into account the relationship between the nuclear quadrupole moment and the deformation, the electric quadrupole moment factor is added to the original three-parameter formula to obtain a new formula for the nuclear charge radius. Fitting the four-parameter formula, it is found that the theoretical value of the nuclear charge radius is in good agreement with the experimental value, the root-mean-square deviation is 0.0397 fm. Considering the relationship between the total spin and the electric quadrupole moment, the intrinsic electric quadrupole moment is obtained and brought into the formula for fitting, and the root-mean-square deviation further decreases,the root-mean-square deviation is 0.0372 fm. Finally, considering the universality of odd-even staggering, we add the <inline-formula><tex-math id="M6">\begin{document}$\delta$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20191643_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20191643_M6.png"/></alternatives></inline-formula> term that can reflect the odd and even oscillation phenomenon, and the root-mean-square deviation obtained by the formula is 0.369 fm, which better reflects the relationship between the deformation and the nuclear charge radius. Compared with the formulas already proposed, the new formula can better reflect the variation trend of nuclear deformation, shell effect, odd-even staggering, etc., and the calculation accuracy is also improved, which can provide a useful reference for future experiments.

Calculations of Quadrupole Deformation Parameters for Nuclei in fp shell

The quadrupole transition rates and intrinsic quadrupole moment are calculated for some fp shell nucleus. For fp-shell nuclei with neutron number N > 20 and with proton number p > 20, fp shell model space and fpd6 effective interaction are used. The calculations are performed using effective charges obtained from Bohr – Mottelson model and also the standard proton and neutron effective charges, and the results are compared with the available experimental values. The results of the quadrupole deformation parameter calculated from transition probabilities are better from the intrinsic quadrupole moment with ST effective charges.

Study the Shapes of Nuclei for Heavy Elements with Mass Number Equal to (226≤A≤252) through Determination of Deformation Parameters for Two Elements (U&Cf)

The current paper focuses on the studying the forms of (even-even) nuclei for the heavy elements with mass numbers in the range from (A=226 - 252) for isotopes. This work will consist of studying deformation parameters which is deduced from the "Reduced Electric Transition Probability" which is in its turn dependent on the first Excited State . The "Intrinsic Electric Quadrupole Moments" (non-spherical charge distribution) were also calculated. In addition to that the Roots Mean Square Radii (Isotope Shift) are accounted for in order to compare them with the theoretical results.
 The difference and variation in shapes of nuclei for the selected isotopes were detected using 3D-plots for them (with symmetric axes); a 2D-plot were also used for each isotope to discriminate between them by the values of semi-major is equal (a) axes and semi minor is equal (b) axes.

The Emergence of Anion-π Catalysis.

The objective of this Account is to summarize the first five years of anion-π catalysis. The general idea of anion-π catalysis is to stabilize anionic transition states on aromatic surfaces. This is complementary to the stabilization of cationic transition states on aromatic surfaces, a mode of action that occurs in nature and is increasingly used in chemistry. Anion-π catalysis, however, rarely occurs in nature and has been unexplored in chemistry. Probably because the attraction of anions to π surfaces as such is counterintuitive, anion-π interactions in general are much younger than cation-π interactions and remain under-recognized until today. Anion-π catalysis has emerged from early findings that anion-π interactions can mediate the transport of anions across lipid bilayer membranes. With this evidence for stabilization in the ground state secured, there was no reason to believe that anion-π interactions could not also stabilize anionic transition states. As an attractive reaction to develop anion-π catalysis, the addition of malonic acid half thioesters to enolate acceptors was selected. This choice was also made because without enzymes decarboxylation is preferred and anion-π interactions promised to catalyze selectively the disfavored but relevant enolate addition. Concerning anion-π catalysts, we started with naphthalene diimides (NDIs) because their intrinsic quadrupole moment is highly positive. The NDI scaffold was used to address questions such as the positioning of substrates on the catalytic π surface or the dependence of activity on the π acidity of this π surface. With the basics in place, the next milestone was the creation of anion-π enzymes, that is, enzymes that operate with an interaction rarely used in biology, at least on intrinsically π-acidic or highly polarizable aromatic amino-acid side chains. Electric-field-assisted anion-π catalysis addresses topics such as heterogeneous catalysis on electrodes and remote control of activity by voltage. On π-stacked foldamers, anion-(π) n-π catalysis was discovered. Fullerenes emerged as the scaffold of choice to explore contributions from polarizability. On fullerenes, anionic transition states are stabilized by large macrodipoles that appear only in response to their presence. With this growing collection of anion-π catalysts, several reactions beyond enolate addition have been explored so far. Initial efforts focused on asymmetric anion-π catalysis. Increasing enantioselectivity with increasing π acidity of the active π surface has been exemplified for enamine and iminium chemistry and for anion-π transaminase mimics. However, the delocalized nature of anion-π interactions calls for the stabilization of charge displacements over longer distances. The first step in this direction was the formation of cyclohexane rings with five stereogenic centers from achiral acyclic substrates on π-acidic surfaces. Moreover, the intrinsically disfavored exo transition state of anionic Diels-Alder reactions is stabilized selectively on π-acidic surfaces; endo products and otherwise preferred Michael addition products are completely suppressed. Taken together, we hope that these results on catalyst design and reaction scope will establish anion-π catalysis as a general principle in catalysis in the broadest sense.

High-energy hyperbolic scattering by neutron stars and black holes

We investigate the hyperbolic scattering of test particles, spinning test particles and particles with spin-induced quadrupolar structure by a Kerr black hole in the ultrarelativistic regime. We also study how the features of the scattering process modify if the source of the background gravitational field is endowed with a nonzero mass quadrupole moment as described by the (approximate) Hartle-Thorne solution. We compute the scattering angle either in closed analytical form, when possible, or as a power series of the (dimensionless) inverse impact parameter. It is a function of the parameters characterizing the source (intrinsic angular momentum and mass quadrupole moment) as well as the scattered body (spin and polarizability constant). Measuring the scattering angle thus provides useful information to determine the nature of the two components of the binary system undergoing high-energy scattering processes.

Elastic and inelastic O16+C12 rainbow scattering within the coupled-channels mechanism

Angular distributions of the differential cross section of $^{16}\mathrm{O}+^{12}\mathrm{C}$ elastic and inelastic scattering in the energy range ${E}_{\mathrm{lab}}=181\ensuremath{-}1503$ MeV were fitted with the full cluster folded approach (DFC1) using the coupled-channels (CC) method by taking into account the effect of the low-lying states, ${0}^{+}$ and ${2}^{+}$ (${E}_{\mathrm{ex}}=4.44$ MeV) for the target nucleus. The cluster transition density is generated macroscopically by deforming the cluster ground state modified Gaussian density distribution of the target nucleus. The coupled-channels calculations with the fitted parameters for the elastic scattering provide a successful description of the inelastic experimental measurements. The obtained results are compared with the finding of the phenomenological Woods-Saxon potential. It was found that the characteristic features of the nuclear rainbow phenomena can be reproduced successfully by our CC calculations with both potentials but fail to reproduce the new Airy minimum of the nuclear rainbow structure. The deduced intrinsic quadrupole moment values, ${Q}_{20}$, derived from the analyses are compared with results of previous studies. The deformation lengths, ${\ensuremath{\delta}}_{20}$, obtained by CC calculations are in agreement with those obtained from the electromagnetic measurement values and those reported in previous studies.

Estimation of geometrical shapes of mass-formed nuclei (A=102-178) from the calculation of deformation parameters for two elements (Sn & Yb)

The present research focused on the studying of even- even nuclei forms for elements with mass numbers greater than 100 (A > 100) for isotopes. Which included the study of deformation parameters (β2) derived from the Reduced Electric Transition Probability B(E2) ↑ based on the energy of the first Excited State (2+), and distortion parameter (δ) from Intrinsic Electric Quadrupole Moments (Q0). Roots Mean Square Radii < r2 >1/2 were also calculated and compared with theoretical values. The diversity of nuclei forms for selected isotopes and their differences was observed by plotting three-dimensional shapes (axially symmetric) in addition to drawing two-dimensional shapes of single element isotopes to distinguish between them by using semi-major (a) and semi minor (b) axes.

Strongly coupled rotational band in Mg33

Author(s): Richard, AL; Crawford, HL; Fallon, P; Macchiavelli, AO; Bader, VM; Bazin, D; Bowry, M; Campbell, CM; Carpenter, MP; Clark, RM; Cromaz, M; Gade, A; Ideguchi, E; Iwasaki, H; Jones, MD; Langer, C; Lee, IY; Loelius, C; Lunderberg, E; Morse, C; Rissanen, J; Salathe, M; Smalley, D; Stroberg, SR; Weisshaar, D; Whitmore, K; Wiens, A; Williams, SJ; Wimmer, K; Yamamato, T | Abstract: The island of inversion at N≈20 for the neon, sodium, and magnesium isotopes has long been an area of interest both experimentally and theoretically due to the subtle competition between 0p-0h and np-nh configurations leading to deformed shapes. However, the presence of rotational band structures, which are fingerprints of deformed shapes, have only recently been observed in this region. In this work, we report on a measurement of the low-lying level structure of Mg33 populated by a two-stage projectile fragmentation reaction and studied with the Gamma Ray Energy Tracking In-Beam Nuclear Array (GRETINA). The experimental level energies, ground-state magnetic moment, intrinsic quadrupole moment, and γ-ray intensities show good agreement with the strong-coupling limit of a rotational model.