Nonrelativistic bound states at finite temperature. II. Muonic hydrogen

We illustrate how to apply modern effective field-theory techniques and dimensional regularization to factorize the various scales, which appear in QED bound states at finite temperature. We focus here on the muonic hydrogen atom. Vacuum polarization effects make the physics of this atom at finite temperature very close to that of heavy quarkonium states. We comment on the implications of our results for these states in the quark gluon plasma. In particular, we estimate the effects of a finite-charm quark mass in the dissociation temperature of bottomonium.

Numerical signs fos a transition in the 2d Random Field Ising Model at T=0

Intensive numerical studies of exact ground states of the two-dimensional ferromagnetic random field Ising model at T=0, with a Gaussian distribution of fields, are presented. Standard finite size scaling analysis of the data suggests the existence of a transition at ¿c=0.64±0.08. Results are compared with existing theories and with the study of metastable avalanches in the same model.

Massless minimally coupled fields in de Sitter space: O(4)-symmetric states versus de Sitter invariant vacuum

The issue of de Sitter invariance for a massless minimally coupled scalar field is examined. Formally, it is possible to construct a de Sitterinvariant state for this case provided that the zero mode of the field is quantized properly. Here we take the point of view that this state is physically acceptable, in the sense that physical observables can be computed and have a reasonable interpretation. In particular, we use this vacuum to derive a new result: that the squared difference between the field at two points along a geodesic observers spacetime path grows linearly with the observers proper time for a quantum state that does not break de Sitter invariance. Also, we use the Hadamard formalism to compute the renormalized expectation value of the energy-momentum tensor, both in the O(4)-invariant states introduced by Allen and Follaci, and in the de Sitterinvariant vacuum. We find that the vacuum energy density in the O(4)-invariant case is larger than in the de Sitterinvariant case.

Effect of a transverse magnetic field on resonant magnetization tunneling in high-spin molecules

The recent observation of steps at regular intervals of magnetic field in the hysteresis loops of oriented crystals of the spin-10 molecular magnet Mn12O12(CH3COO)16(H2O)4 has been attributed to resonant tunneling between spin states. Here, we investigate the effect on the relaxation rate of applying the magnetic field at an angle with respect to the easy axis of magnetization. We find that the position of the resonances is independent of the transverse component of the field, and is determined solely by the longitudinal component. On the other hand, a transverse field significantly increases the relaxation rate, both on and off resonance. We discuss classical and quantum mechanical interpretations of this effect

Quantum decay of metastable states in small magnetic particles

We present an imaginary-time path-integral study of the problem of quantum decay of a metastable state of a uniaxial magnetic particle placed in the magnetic field at an arbitrary angle. Our findings agree with earlier results of Zaslavskii obtained by mapping the spin Hamiltonian onto a particle Hamiltonian. In the limit of low barrier, weak dependence of the decay rate on the angle is found, except for the field which is almost normal to the anisotropy axis, where the rate is sharply peaked, and for the field approaching the parallel orientation, where the rate rapidly goes to zero. This distinct angular dependence, together with the dependence of the rate on the field strength, provides an independent test for macroscopic spin tunneling.

Field Testing and Evaluation of a Demonstration Timber Bridge, February 2012

Asphalt wearing surfaces are commonly used on timber bridges with transverse glued-laminated deck panel systems to help protect the timber components. However, poor performance of these asphalt wearing surfaces in the past has resulted in repeated repair and increased maintenance costs. This report describes the field demonstration and testing of a newly-constructed, glued-laminated timber girder bridge. Previous field work revealed that differential panel deflections in the glued-laminated deck were one significant factor resulting in the premature failure of the asphalt wearing surfaces on these bridges. In addition, laboratory work subsequent to the field testing attempted to address the problematic asphalt cracking common in transverse glued-laminated panel decks by testing several deck joint connection alternatives. The field demonstration project described in this report showcases the retrofit detail that was determined to provide the best field performance. The project was a cooperative effort between the Bridge Engineering Center (BEC) at Iowa State University and the United States Department of Agriculture (USDA) Forest Service Forest Products Laboratory (FPL).

Neutral atoms in ionic lattices: Excited states of KCl:Ag(0)

The optical-absorption spectrum of a cationic Ag0 atom in a KCl crystal has been studied theoretically by means of a series of cluster models of increasing size. Excitation energies have been determined by means of a multiconfigurational self-consistent field procedure followed by a second-order perturbation correlation treatment. Moreover results obtained within the density-functional framework are also reported. The calculations confirm the assignment of bands I and IV to transitions of the Ag-5s electron into delocalized states with mainly K-4s,4p character. Bands II and III have been assigned to internal transitions on the Ag atom, which correspond to the atomic Ag-4d to Ag-5s transition. We also determine the lowest charge transfer (CT) excitation energy and confirm the assignment of band VI to such a transition. The study of the variation of the CT excitation energy with the Ag-Cl distance R gives additional support to a large displacement of the Cl ions due to the presence of the Ag0 impurity. Moreover, from the present results, it is predicted that on passing to NaCl:Ag0 the CT onset would be out of the optical range while the 5s-5p transition would undergo a redshift of 0.3 eV. These conclusions, which underline the different character of involved orbitals, are consistent with experimental findings. The existence of a CT transition in the optical range for an atom inside an ionic host is explained by a simple model, which also accounts for the differences with the more common 3d systems. The present study sheds also some light on the R dependence of the s2-sp transitions due to s2 ions like Tl+.

Evaluation of Recycled Rubber in Asphalt Cement Concrete - Field Testing, Final Report for HR-330, 330A, 330B, 330C, 330D, 2002

Roughly 242 million used tires are generated annually in the United States. Many of these tires end up being landfilled or stockpiled. The stockpiles are unsightly, unsanitary, and also collect water which creates the perfect breeding ground for mosquitoes, some of which carry disease. In an effort to reduce the number of used tire stockpiles the federal government mandated the use of recycled rubber in federally funded, state implemented department of transportation (DOT) projects. This mandate required the use of recycled rubber in 5% of the asphalt cement concrete (ACC) tonnage used in federally funded projects in 1994, increasing that amount by 5% each year until 20% was reached, and remaining at 20% thereafter. The mandate was removed as part of the appropriations process in 1994, after the projects in this research had been completed. This report covers five separate projects that were constructed by the Iowa Department Of Transportation (DOT) in 1991 and 1992. These projects had all had some form of rubber incorporated into their construction and were evaluated for 5 years. The conclusion of the study is that the pavements with tire rubber added performed essentially the same as conventional ACC pavement. An exception was the use of rubber chips in a surface lift. This performed better at crack control and worse with friction values than conventional ACC. The cost of the pavement with rubber additive was significantly higher. As a result, the benefits do not outweigh the costs of using this recycled rubber process in pavements in Iowa.

Field Evaluation of Pavement Marking Materials, MLR-79-02, 1979

Pavement marking materials other than conventional paint must be evaluated as environmental standards become more restrictive. The new EPA classification for solvents states that all oil paints are photochemically reactive and, therefore, contribute to smog. This will eventually result in the elimination of organic solvents from all paints, which may occur in Iowa by 1985. The Special Investigations Section of the Office of Materials field reviewed all urban and rural applications of pavement marking materials in the spring of 1979. The field review consisted of a visual estimation of percent marking missing, percent satisfactory, and percent non-satisfactory; reflective readings by ERMA; and notation of special conditions which may have impacted performance. ERMA was not effective in evaluating the reflective quality of pavement marking materials. No pavement marking materials evaluated have been successful enough to date to totally replace conventional painting methods.

Design, Construction, and Field Testing of an Ultra High Performance Concrete Pi-Girder Bridge, TR-574, 2011

Among the variety of road users and vehicle types that travel on U.S. public roadways, slow moving vehicles (SMVs) present unique safety and operations issues. SMVs include vehicles that do not maintain a constant speed of 25 mph, such as large farm equipment, construction vehicles, or horse-drawn buggies. Though the number of crashes involving SMVs is relatively small, SMV crashes tend to be severe. Additionally, SMVs can be encountered regularly on non-Interstate/non-expressway public roadways, but motorists may not be accustomed to these vehicles. This project was designed to improve transportation safety for SMVs on Iowa’s public roadway system. This report includes a literature review that shows various SMV statistics and laws across the United States, a crash study based on three years of Iowa SMV crash data, and recommendations from the SMV community.

Field and Laboratory Evaluation of Precast Concrete Bridges, TR-440, 2001

Recent data compiled by the National Bridge Inventory revealed 29% of Iowa's approximate 24,600 bridges were either structurally deficient or functionally obsolete. This large number of deficient bridges and the high cost of needed repairs create unique problems for Iowa and many other states. The research objective of this project was to determine the load capacity of a particular type of deteriorating bridge – the precast concrete deck bridge – which is commonly found on Iowa's secondary roads. The number of these precast concrete structures requiring load postings and/or replacement can be significantly reduced if the deteriorated structures are found to have adequate load capacity or can be reliably evaluated. Approximately 600 precast concrete deck bridges (PCDBs) exist in Iowa. A typical PCDB span is 19 to 36 ft long and consists of eight to ten simply supported precast panels. Bolts and either a pipe shear key or a grouted shear key are used to join adjacent panels. The panels resemble a steel channel in cross-section; the web is orientated horizontally and forms the roadway deck and the legs act as shallow beams. The primary longitudinal reinforcing steel bundled in each of the legs frequently corrodes and causes longitudinal cracks in the concrete and spalling. The research team performed service load tests on four deteriorated PCDBs; two with shear keys in place and two without. Conventional strain gages were used to measure strains in both the steel and concrete, and transducers were used to measure vertical deflections. Based on the field results, it was determined that these bridges have sufficient lateral load distribution and adequate strength when shear keys are properly installed between adjacent panels. The measured lateral load distribution factors are larger than AASHTO values when shear keys were not installed. Since some of the reinforcement had hooks, deterioration of the reinforcement has a minimal affect on the service level performance of the bridges when there is minimal loss of cross-sectional area. Laboratory tests were performed on the PCDB panels obtained from three bridge replacement projects. Twelve deteriorated panels were loaded to failure in a four point bending arrangement. Although the panels had significant deflections prior to failure, the experimental capacity of eleven panels exceeded the theoretical capacity. Experimental capacity of the twelfth panel, an extremely distressed panel, was only slightly below the theoretical capacity. Service tests and an ultimate strength test were performed on a laboratory bridge model consisting of four joined panels to determine the effect of various shear connection configurations. These data were used to validate a PCDB finite element model that can provide more accurate live load distribution factors for use in rating calculations. Finally, a strengthening system was developed and tested for use in situations where one or more panels of an existing PCDB need strengthening.

Field Testing of Integral Abutments, Interim Report, HR-399, 1998

Integral abutment bridges are constructed without an expansion joint in the superstructure of the bridge; therefore, the bridge girders, deck, abutment diaphragms, and abutments are monolithically constructed. The abutment piles in an integral abutment bridge are vertically orientated, and they are embedded into the pile cap. When this type of a bridge experiences thermal expansion or contraction, horizontal displacements are induced at the top of the abutment piles. The flexibility of the abutment piles eliminates the need to provide an expansion joint at the inside face to the abutments: Integral abutment bridge construction has been used in Iowa and other states for many years. This research is evaluating the performance of integral abutment bridges by investigating thermally induced displacements, strains, and temperatures in two Iowa bridges. Each bridge has a skewed alignment, contains five prestressed concrete girders that support a 30-ft wide roadway for three spans, and involves a water crossing. The bridges will be monitored for about two years. For each bridge, an instrumentation package includes measurement devices and hardware and software support systems. The measurement devices are displacement transducers, strain gages, and thermocouples. The hardware and software systems include a data-logger; multiplexers; directline telephone service and computer terminal modem; direct-line electrical power; lap-top computer; and an assortment of computer programs for monitoring, transmitting, and management of the data. Instrumentation has been installed on a bridge located in Guthrie County, and similar instrumentation is currently being installed on a bridge located in Story County. Preliminary test results for the bridge located in Guthrie County have revealed that temperature changes of the bridge deck and girders induce both longitudinal and transverse displacements of the abutments and significant flexural strains in the abutment piles. For an average temperature range of 73° F for the superstructure concrete in the bridge located in Guthrie County, the change in the bridge length was about 1 118 in. and the maximum, strong-axis, flexural-strain range for one of the abutment piles was about 400 micro-strains, which corresponds to a stress range of about 11,600 psi.

Mycelial compatibility and aggressiveness of Sclerotinia sclerotiorum isolates from Brazil and the United States

The objective of this work was to evaluate the genetic diversity among Sclerotinia sclerotiorum isolates from Brazil and the USA, assess their aggressiveness variability, and verify the existence of an isolate-cultivar interaction. Isolate variability was determined by mycelial compatibility grouping (MCG), and isolate aggressiveness by cut-stem inoculations of soybean cultivars. Two experiments for MCGs and two for aggressiveness were conducted with two sets of isolates. The first set included nine isolates from the same soybean field in Brazil and nine from the Midwest region of the USA. The second set included 16 isolates from several regions of Brazil and one from the USA. In the first set, 18 isolates formed 12 different MCGs. In the second set, 81% of the isolates from Brazil grouped into a single MCG. No common MCGs were observed among isolates from Brazil and the USA. The isolates showed aggressiveness differences in the first set, but not in the second. Although aggressiveness differed in the first set, soybean cultivars and isolates did not interact significantly. Cultivar rank remained the same, regardless of the genetic diversity, aggressiveness difference, and region or country of origin of the isolate. Results from screening of soybean cultivars, performed by the cut-stem method in the USA, can be used as reference for researchers in Brazil.

The Role of Transnational Elites in shaping the evolving Field of Internet Governance

La gouvernance de l'Internet est une thématique récente dans la politique mondiale. Néanmoins, elle est devenue au fil des années un enjeu économique et politique important. La question a même pris une importance particulière au cours des derniers mois en devenant un sujet d'actualité récurrent. Forte de ce constat, c ette recherche retrace l'histoire de la gouvernance de l'Internet depuis son émergence comme enjeu politique dans les années 1980 jusqu'à la fin du Sommet Mondial sur la Société de l'Information (SMSI) en 2005. Plutôt que de se focaliser sur l'une ou l'autre des institutions impliquées dans la régulation du réseau informatique mondial, cette recherche analyse l'émergence et l'évolution historique d'un espace de luttes rassemblant un nombre croissant d'acteurs différents. Cette évolution est décrite à travers le prisme de la relation dialectique entre élites et non-élites et de la lutte autour de la définition de la gouvernance de l'Internet. Cette thèse explore donc la question de comment les relations au sein des élites de la gouvernance de l'Internet et entre ces élites et les non-élites expliquent l'emergence, l'évolution et la structuration d'un champ relativement autonome de la politique mondiale centré sur la gouvernance de l'Internet. Contre les perspectives dominantes réaliste et libérales, cette recherche s'ancre dans une approche issue de la combinaison des traditions hétérodoxes en économie politique internationale et des apports de la sociologie politique internationale. Celle-ci s'articule autour des concepts de champ, d'élites et d'hégémonie. Le concept de champ, développé par Bourdieu inspire un nombre croissant d'études de la politique mondiale. Il permet à la fois une étude différenciée de la mondialisation et l'émergence d'espaces de lutte et de domination au niveau transnational. La sociologie des élites, elle, permet une approche pragmatique et centrée sur les acteurs des questions de pouvoir dans la mondialisation. Cette recherche utilise plus particulièrement le concept d'élite du pouvoir de Wright Mills pour étudier l'unification d'élites a priori différentes autour de projets communs. Enfin, cette étude reprend le concept néo-gramscien d'hégémonie afin d'étudier à la fois la stabilité relative du pouvoir d'une élite garantie par la dimension consensuelle de la domination, et les germes de changement contenus dans tout ordre international. A travers l'étude des documents produits au cours de la période étudiée et en s'appuyant sur la création de bases de données sur les réseaux d'acteurs, cette étude s'intéresse aux débats qui ont suivi la commercialisation du réseau au début des années 1990 et aux négociations lors du SMSI. La première période a abouti à la création de l'Internet Corporation for Assigned Names and Numbers (ICANN) en 1998. Cette création est le résultat de la recherche d'un consensus entre les discours dominants des années 1990. C'est également le fruit d'une coalition entre intérêts au sein d'une élite du pouvoir de la gouvernance de l'Internet. Cependant, cette institutionnalisation de l'Internet autour de l'ICANN excluait un certain nombre d'acteurs et de discours qui ont depuis tenté de renverser cet ordre. Le SMSI a été le cadre de la remise en cause du mode de gouvernance de l'Internet par les États exclus du système, des universitaires et certaines ONG et organisations internationales. C'est pourquoi le SMSI constitue la seconde période historique étudiée dans cette thèse. La confrontation lors du SMSI a donné lieu à une reconfiguration de l'élite du pouvoir de la gouvernance de l'Internet ainsi qu'à une redéfinition des frontières du champ. Un nouveau projet hégémonique a vu le jour autour d'éléments discursifs tels que le multipartenariat et autour d'insitutions telles que le Forum sur la Gouvernance de l'Internet. Le succès relatif de ce projet a permis une stabilité insitutionnelle inédite depuis la fin du SMSI et une acceptation du discours des élites par un grand nombre d'acteurs du champ. Ce n'est que récemment que cet ordre a été remis en cause par les pouvoirs émergents dans la gouvernance de l'Internet. Cette thèse cherche à contribuer au débat scientifique sur trois plans. Sur le plan théorique, elle contribue à l'essor d'un dialogue entre approches d'économie politique mondiale et de sociologie politique internationale afin d'étudier à la fois les dynamiques structurelles liées au processus de mondialisation et les pratiques localisées des acteurs dans un domaine précis. Elle insiste notamment sur l'apport de les notions de champ et d'élite du pouvoir et sur leur compatibilité avec les anlayses néo-gramsciennes de l'hégémonie. Sur le plan méthodologique, ce dialogue se traduit par une utilisation de méthodes sociologiques telles que l'anlyse de réseaux d'acteurs et de déclarations pour compléter l'analyse qualitative de documents. Enfin, sur le plan empirique, cette recherche offre une perspective originale sur la gouvernance de l'Internet en insistant sur sa dimension historique, en démontrant la fragilité du concept de gouvernance multipartenaire (multistakeholder) et en se focalisant sur les rapports de pouvoir et les liens entre gouvernance de l'Internet et mondialisation. - Internet governance is a recent issue in global politics. However, it gradually became a major political and economic issue. It recently became even more important and now appears regularly in the news. Against this background, this research outlines the history of Internet governance from its emergence as a political issue in the 1980s to the end of the World Summit on the Information Society (WSIS) in 2005. Rather than focusing on one or the other institution involved in Internet governance, this research analyses the emergence and historical evolution of a space of struggle affecting a growing number of different actors. This evolution is described through the analysis of the dialectical relation between elites and non-elites and through the struggle around the definition of Internet governance. The thesis explores the question of how the relations among the elites of Internet governance and between these elites and non-elites explain the emergence, the evolution, and the structuration of a relatively autonomous field of world politics centred around Internet governance. Against dominant realist and liberal perspectives, this research draws upon a cross-fertilisation of heterodox international political economy and international political sociology. This approach focuses on concepts such as field, elites and hegemony. The concept of field, as developed by Bourdieu, is increasingly used in International Relations to build a differentiated analysis of globalisation and to describe the emergence of transnational spaces of struggle and domination. Elite sociology allows for a pragmatic actor-centred analysis of the issue of power in the globalisation process. This research particularly draws on Wright Mill's concept of power elite in order to explore the unification of different elites around shared projects. Finally, this thesis uses the Neo-Gramscian concept of hegemony in order to study both the consensual dimension of domination and the prospect of change contained in any international order. Through the analysis of the documents produced within the analysed period, and through the creation of databases of networks of actors, this research focuses on the debates that followed the commercialisation of the Internet throughout the 1990s and during the WSIS. The first time period led to the creation of the Internet Corporation for Assigned Names and Numbers (ICANN) in 1998. This creation resulted from the consensus-building between the dominant discourses of the time. It also resulted from the coalition of interests among an emerging power elite. However, this institutionalisation of Internet governance around the ICANN excluded a number of actors and discourses that resisted this mode of governance. The WSIS became the institutional framework within which the governance system was questioned by some excluded states, scholars, NGOs and intergovernmental organisations. The confrontation between the power elite and counter-elites during the WSIS triggered a reconfiguration of the power elite as well as a re-definition of the boundaries of the field. A new hegemonic project emerged around discursive elements such as the idea of multistakeholderism and institutional elements such as the Internet Governance Forum. The relative success of the hegemonic project allowed for a certain stability within the field and an acceptance by most non-elites of the new order. It is only recently that this order began to be questioned by the emerging powers of Internet governance. This research provides three main contributions to the scientific debate. On the theoretical level, it contributes to the emergence of a dialogue between International Political Economy and International Political Sociology perspectives in order to analyse both the structural trends of the globalisation process and the located practices of actors in a given issue-area. It notably stresses the contribution of concepts such as field and power elite and their compatibility with a Neo-Gramscian framework to analyse hegemony. On the methodological level, this perspective relies on the use of mixed methods, combining qualitative content analysis with social network analysis of actors and statements. Finally, on the empirical level, this research provides an original perspective on Internet governance. It stresses the historical dimension of current Internet governance arrangements. It also criticise the notion of multistakeholde ism and focuses instead on the power dynamics and the relation between Internet governance and globalisation.

Quantum transport phenomena and shallow impurity states in CdSb

This work is dedicated to investigation of the energy spectrum of one of the most anisotropic narrow-gap semiconductors, CdSb. At the beginning of the present studies even the model of its energy band structure was not clear. Measurements of galvanomagnetic effects in wide temperature range (1.6 - 300 K) and in magnetic fields up to 30 T were chosen for clarifying of the energy spectrum in the intentionally undoped CdSb single crystals and doped with shallow impurities (In, Ag). Detection of the Shubnikov - de Haas oscillations allowed estimating the fundamental energy spectrum parameters. The shapes of the Fermi surfaces of electrons (sphere) and holes (ellipsoid), the number of the equivalent extremums for valence band (2) and their positions in the Brillouin zone were determined for the first time in this work. Also anisotropy coefficients, components of the tensor of effective masses of carriers, effective masses of density of states, nonparabolicity of the conduction and valence bands, g-factor and its anisotropy for n- and p-CdSb were estimated for the first time during these studies. All the results obtained are compared with the cyclotron resonance data and the corresponding theoretical calculations for p-CdSb. This is basic information for the analyses of the complex transport properties of CdSb and for working out the energy spectrum model of the shallow energy levels of defects and impurities in this semiconductor. It was found out existence of different mechanisms of hopping conductivity in the presence of metal - insulator transition induced by magnetic field in n- and p-CdSb. Quite unusual feature opened in CdSb is that different types of hopping conductivity may take place in the same crystal depending on temperature, magnetic field or even orientation of crystal in magnetic field. Transport properties of undoped p-CdSb samples show that the anisotropy of the resistivity in weak and strong magnetic fields is determined completely by the anisotropy of the effective mass of the holes. Temperature and magnetic field dependence of the Hall coefficient and magnetoresistance is attributed to presence of two groups of holes with different concentrations and mobilities. The analysis demonstrates that below Tcr ~ 20 K and down to ~ 6 - 7 K the low-mobile carriers are itinerant holes with energy E2 ≈ 6 meV. The high-mobile carriers, at all temperatures T < Tcr, are holes activated thermally from a deeper acceptor band to itinerant states of a shallower acceptor band with energy E1 ≈ 3 meV. Analysis of temperature dependences of mobilities confirms the existence of the heavy-hole band or a non-equivalent maximum and two equivalent maxima of the light-hole valence band. Galvanomagnetic effects in n-CdSb reveal the existence of two groups of carriers. These are the electrons of a single minimum in isotropic conduction band and the itinerant electrons of the narrow impurity band, having at low temperatures the energies above the bottom of the conduction band. It is found that above this impurity band exists second impurity band of only localized states and the energy of both impurity bands depend on temperature so that they sink into the band gap when temperature is increased. The bands are splitted by the spin, and in strong magnetic fields the energy difference between them decreases and redistribution of the electrons between the two impurity bands takes place. Mobility of the conduction band carriers demonstrates that scattering in n-CdSb at low temperatures is strongly anisotropic. This is because of domination from scattering on the neutral impurity centers and increasing of the contribution to mobility from scattering by acoustic phonons when temperature increases. Metallic conductivity in zero or weak magnetic field is changed to activated conductivity with increasing of magnetic field. This exhibits a metal-insulator transition (MIT) induced by the magnetic field due to shift of the Fermi level from the interval of extended states to that of the localized states of the electron spectrum near the edge of the conduction band. The Mott variablerange hopping conductivity is observed in the low- and high-field intervals on the insulating side of the MIT. The results yield information about the density of states, the localization radius of the resonant impurity band with completely localized states and about the donor band. In high magnetic fields this band is separated from the conduction band and lies below the resonant impurity bands.